diff --git a/mlir/include/mlir/IR/BasicBlock.h b/mlir/include/mlir/IR/BasicBlock.h
index 487c1bb63a4d..1b38a5eaa042 100644
--- a/mlir/include/mlir/IR/BasicBlock.h
+++ b/mlir/include/mlir/IR/BasicBlock.h
@@ -47,7 +47,7 @@ public:
   CFGFunction *getParent() { return function; }
 
   //===--------------------------------------------------------------------===//
-  // Block arguments management
+  // Block argument management
   //===--------------------------------------------------------------------===//
 
   // This is the list of arguments to the block.
diff --git a/mlir/include/mlir/IR/CFGValue.h b/mlir/include/mlir/IR/CFGValue.h
index d0140f3a3674..8dd3f96d5641 100644
--- a/mlir/include/mlir/IR/CFGValue.h
+++ b/mlir/include/mlir/IR/CFGValue.h
@@ -51,6 +51,7 @@ public:
       return true;
 
     case SSAValueKind::MLFuncArgument:
+    case SSAValueKind::BlockArgument:
     case SSAValueKind::StmtResult:
     case SSAValueKind::ForStmt:
       return false;
diff --git a/mlir/include/mlir/IR/MLValue.h b/mlir/include/mlir/IR/MLValue.h
index 0c6c0b226963..847bd1bccf0d 100644
--- a/mlir/include/mlir/IR/MLValue.h
+++ b/mlir/include/mlir/IR/MLValue.h
@@ -25,16 +25,18 @@
 #include "mlir/IR/SSAValue.h"
 
 namespace mlir {
-class MLValue;
-class Statement;
-class MLFunction;
 class ForStmt;
+class MLValue;
+class MLFunction;
+class Statement;
+class StmtBlock;
 
 /// This enum contains all of the SSA value kinds that are valid in an ML
 /// function.  This should be kept as a proper subtype of SSAValueKind,
 /// including having all of the values of the enumerators align.
 enum class MLValueKind {
   MLFuncArgument = (int)SSAValueKind::MLFuncArgument,
+  BlockArgument = (int)SSAValueKind::BlockArgument,
   StmtResult = (int)SSAValueKind::StmtResult,
   ForStmt = (int)SSAValueKind::ForStmt,
 };
@@ -54,6 +56,7 @@ public:
   static bool classof(const SSAValue *value) {
     switch (value->getKind()) {
     case SSAValueKind::MLFuncArgument:
+    case SSAValueKind::BlockArgument:
     case SSAValueKind::StmtResult:
     case SSAValueKind::ForStmt:
       return true;
@@ -102,6 +105,33 @@ private:
   MLFunction *const owner;
 };
 
+/// Block arguments are ML Values.
+class BlockArgument : public MLValue {
+public:
+  static bool classof(const SSAValue *value) {
+    return value->getKind() == SSAValueKind::BlockArgument;
+  }
+
+  /// Return the function that this argument is defined in.
+  MLFunction *getFunction();
+  const MLFunction *getFunction() const {
+    return const_cast<BlockArgument *>(this)->getFunction();
+  }
+
+  StmtBlock *getOwner() { return owner; }
+  const StmtBlock *getOwner() const { return owner; }
+
+private:
+  friend class StmtBlock; // For access to private constructor.
+  BlockArgument(Type type, StmtBlock *owner)
+      : MLValue(MLValueKind::BlockArgument, type), owner(owner) {}
+
+  /// The owner of this operand.
+  /// TODO: can encode this more efficiently to avoid the space hit of this
+  /// through bitpacking shenanigans.
+  StmtBlock *const owner;
+};
+
 /// This is a value defined by a result of an operation instruction.
 class StmtResult : public MLValue {
 public:
diff --git a/mlir/include/mlir/IR/SSAValue.h b/mlir/include/mlir/IR/SSAValue.h
index 29bc6f034c50..919429b209a5 100644
--- a/mlir/include/mlir/IR/SSAValue.h
+++ b/mlir/include/mlir/IR/SSAValue.h
@@ -37,6 +37,7 @@ enum class SSAValueKind {
   BBArgument,     // basic block argument
   InstResult,     // instruction result
   MLFuncArgument, // ML function argument
+  BlockArgument,  // Block argument
   StmtResult,     // statement result
   ForStmt,        // for statement induction variable
 };
diff --git a/mlir/include/mlir/IR/Statement.h b/mlir/include/mlir/IR/Statement.h
index 8b5dce7aad81..d6576d32486e 100644
--- a/mlir/include/mlir/IR/Statement.h
+++ b/mlir/include/mlir/IR/Statement.h
@@ -34,6 +34,10 @@ class MLFunction;
 class StmtBlock;
 class ForStmt;
 class MLIRContext;
+
+/// The operand of a Terminator contains a StmtBlock.
+using StmtBlockOperand = IROperandImpl<StmtBlock, OperationStmt>;
+
 } // namespace mlir
 
 //===----------------------------------------------------------------------===//
diff --git a/mlir/include/mlir/IR/Statements.h b/mlir/include/mlir/IR/Statements.h
index 6b8aa0355c5a..2e07bfb8d32b 100644
--- a/mlir/include/mlir/IR/Statements.h
+++ b/mlir/include/mlir/IR/Statements.h
@@ -24,10 +24,7 @@
 
 #include "mlir/IR/AffineMap.h"
 #include "mlir/IR/IntegerSet.h"
-#include "mlir/IR/MLValue.h"
-#include "mlir/IR/Operation.h"
 #include "mlir/IR/StmtBlock.h"
-#include "mlir/Support/LLVM.h"
 #include "llvm/Support/TrailingObjects.h"
 
 namespace mlir {
@@ -36,9 +33,6 @@ class IntegerSet;
 class AffineCondition;
 class OperationStmt;
 
-/// The operand of a Terminator contains a StmtBlock.
-using StmtBlockOperand = IROperandImpl<StmtBlock, OperationStmt>;
-
 /// Operation statements represent operations inside ML functions.
 class OperationStmt final
     : public Operation,
diff --git a/mlir/include/mlir/IR/StmtBlock.h b/mlir/include/mlir/IR/StmtBlock.h
index c9f2638d56d2..65e0f19066e3 100644
--- a/mlir/include/mlir/IR/StmtBlock.h
+++ b/mlir/include/mlir/IR/StmtBlock.h
@@ -29,6 +29,11 @@ class MLFunction;
 class IfStmt;
 class MLValue;
 
+// TODO(clattner): drop the Stmt prefixes on these once BasicBlock's versions of
+// these go away.
+template <typename BlockType> class StmtPredecessorIterator;
+template <typename BlockType> class StmtSuccessorIterator;
+
 /// Statement block represents an ordered list of statements, with the order
 /// being the contiguous lexical order in which the statements appear as
 /// children of a parent statement in the ML Function.
@@ -40,7 +45,7 @@ public:
     IfClause // IfClause
   };
 
-  ~StmtBlock() { clear(); }
+  ~StmtBlock();
 
   void clear() {
     // Clear statements in the reverse order so that uses are destroyed
@@ -63,6 +68,36 @@ public:
   /// The function is determined by traversing the chain of parent statements.
   MLFunction *findFunction() const;
 
+  //===--------------------------------------------------------------------===//
+  // Block argument management
+  //===--------------------------------------------------------------------===//
+
+  // This is the list of arguments to the block.
+  using BlockArgListType = ArrayRef<BlockArgument *>;
+  BlockArgListType getArguments() const { return arguments; }
+
+  using args_iterator = BlockArgListType::iterator;
+  using reverse_args_iterator = BlockArgListType::reverse_iterator;
+  args_iterator args_begin() const { return getArguments().begin(); }
+  args_iterator args_end() const { return getArguments().end(); }
+  reverse_args_iterator args_rbegin() const { return getArguments().rbegin(); }
+  reverse_args_iterator args_rend() const { return getArguments().rend(); }
+
+  bool args_empty() const { return arguments.empty(); }
+
+  /// Add one value to the argument list.
+  BlockArgument *addArgument(Type type);
+
+  /// Add one argument to the argument list for each type specified in the list.
+  llvm::iterator_range<args_iterator> addArguments(ArrayRef<Type> types);
+
+  /// Erase the argument at 'index' and remove it from the argument list.
+  void eraseArgument(unsigned index);
+
+  unsigned getNumArguments() const { return arguments.size(); }
+  BlockArgument *getArgument(unsigned i) { return arguments[i]; }
+  const BlockArgument *getArgument(unsigned i) const { return arguments[i]; }
+
   //===--------------------------------------------------------------------===//
   // Statement list management
   //===--------------------------------------------------------------------===//
@@ -100,19 +135,10 @@ public:
     return const_cast<StmtBlock *>(this)->front();
   }
 
-  /// getSublistAccess() - Returns pointer to member of statement list
-  static StmtListType StmtBlock::*getSublistAccess(Statement *) {
-    return &StmtBlock::statements;
-  }
-
-  /// These have unconventional names to avoid derive class ambiguities.
-  void printBlock(raw_ostream &os) const;
-  void dumpBlock() const;
-
   /// Returns the statement's position in this block or -1 if the statement is
   /// not present.
-  int findStmtPosInBlock(const Statement &stmt) const {
-    unsigned j = 0;
+  int64_t findStmtPosInBlock(const Statement &stmt) const {
+    int64_t j = 0;
     for (const auto &s : statements) {
       if (&s == &stmt)
         return j;
@@ -129,6 +155,75 @@ public:
     return const_cast<Statement *>(findAncestorStmtInBlock(*stmt));
   }
 
+  //===--------------------------------------------------------------------===//
+  // Terminator management
+  //===--------------------------------------------------------------------===//
+
+  /// Get the terminator instruction of this block, or null if the block is
+  /// malformed.
+  OperationStmt *getTerminator();
+
+  const OperationStmt *getTerminator() const {
+    return const_cast<StmtBlock *>(this)->getTerminator();
+  }
+
+  //===--------------------------------------------------------------------===//
+  // Predecessors and successors.
+  //===--------------------------------------------------------------------===//
+
+  // Predecessor iteration.
+  using const_pred_iterator = StmtPredecessorIterator<const StmtBlock>;
+  const_pred_iterator pred_begin() const;
+  const_pred_iterator pred_end() const;
+  llvm::iterator_range<const_pred_iterator> getPredecessors() const;
+
+  using pred_iterator = StmtPredecessorIterator<StmtBlock>;
+  pred_iterator pred_begin();
+  pred_iterator pred_end();
+  llvm::iterator_range<pred_iterator> getPredecessors();
+
+  /// Return true if this block has no predecessors.
+  bool hasNoPredecessors() const;
+
+  /// If this block has exactly one predecessor, return it.  Otherwise, return
+  /// null.
+  ///
+  /// Note that if a block has duplicate predecessors from a single block (e.g.
+  /// if you have a conditional branch with the same block as the true/false
+  /// destinations) is not considered to be a single predecessor.
+  StmtBlock *getSinglePredecessor();
+
+  const StmtBlock *getSinglePredecessor() const {
+    return const_cast<StmtBlock *>(this)->getSinglePredecessor();
+  }
+
+  // Indexed successor access.
+  unsigned getNumSuccessors() const;
+  const StmtBlock *getSuccessor(unsigned i) const {
+    return const_cast<StmtBlock *>(this)->getSuccessor(i);
+  }
+  StmtBlock *getSuccessor(unsigned i);
+
+  // Successor iteration.
+  using const_succ_iterator = StmtSuccessorIterator<const StmtBlock>;
+  const_succ_iterator succ_begin() const;
+  const_succ_iterator succ_end() const;
+  llvm::iterator_range<const_succ_iterator> getSuccessors() const;
+
+  using succ_iterator = StmtSuccessorIterator<StmtBlock>;
+  succ_iterator succ_begin();
+  succ_iterator succ_end();
+  llvm::iterator_range<succ_iterator> getSuccessors();
+
+  /// getSublistAccess() - Returns pointer to member of statement list
+  static StmtListType StmtBlock::*getSublistAccess(Statement *) {
+    return &StmtBlock::statements;
+  }
+
+  /// These have unconventional names to avoid derive class ambiguities.
+  void printBlock(raw_ostream &os) const;
+  void dumpBlock() const;
+
 protected:
   StmtBlock(StmtBlockKind kind) : kind(kind) {}
 
@@ -137,9 +232,142 @@ private:
   /// This is the list of statements in the block.
   StmtListType statements;
 
+  /// This is the list of arguments to the block.
+  std::vector<BlockArgument *> arguments;
+
   StmtBlock(const StmtBlock &) = delete;
   void operator=(const StmtBlock &) = delete;
 };
 
+//===----------------------------------------------------------------------===//
+// Predecessors
+//===----------------------------------------------------------------------===//
+
+/// Implement a predecessor iterator as a forward iterator.  This works by
+/// walking the use lists of the blocks.  The entries on this list are the
+/// StmtBlockOperands that are embedded into terminator instructions.  From the
+/// operand, we can get the terminator that contains it, and it's parent block
+/// is the predecessor.
+template <typename BlockType>
+class StmtPredecessorIterator
+    : public llvm::iterator_facade_base<StmtPredecessorIterator<BlockType>,
+                                        std::forward_iterator_tag,
+                                        BlockType *> {
+public:
+  StmtPredecessorIterator(StmtBlockOperand *firstOperand)
+      : bbUseIterator(firstOperand) {}
+
+  StmtPredecessorIterator &operator=(const StmtPredecessorIterator &rhs) {
+    bbUseIterator = rhs.bbUseIterator;
+  }
+
+  bool operator==(const StmtPredecessorIterator &rhs) const {
+    return bbUseIterator == rhs.bbUseIterator;
+  }
+
+  BlockType *operator*() const {
+    // The use iterator points to an operand of a terminator.  The predecessor
+    // we return is the block that the terminator is embedded into.
+    return bbUseIterator.getUser()->getBlock();
+  }
+
+  StmtPredecessorIterator &operator++() {
+    ++bbUseIterator;
+    return *this;
+  }
+
+  /// Get the successor number in the predecessor terminator.
+  unsigned getSuccessorIndex() const {
+    return bbUseIterator->getOperandNumber();
+  }
+
+private:
+  using BBUseIterator = SSAValueUseIterator<StmtBlockOperand, OperationStmt>;
+  BBUseIterator bbUseIterator;
+};
+
+inline auto StmtBlock::pred_begin() const -> const_pred_iterator {
+  return const_pred_iterator((StmtBlockOperand *)getFirstUse());
+}
+
+inline auto StmtBlock::pred_end() const -> const_pred_iterator {
+  return const_pred_iterator(nullptr);
+}
+
+inline auto StmtBlock::getPredecessors() const
+    -> llvm::iterator_range<const_pred_iterator> {
+  return {pred_begin(), pred_end()};
+}
+
+inline auto StmtBlock::pred_begin() -> pred_iterator {
+  return pred_iterator((StmtBlockOperand *)getFirstUse());
+}
+
+inline auto StmtBlock::pred_end() -> pred_iterator {
+  return pred_iterator(nullptr);
+}
+
+inline auto StmtBlock::getPredecessors()
+    -> llvm::iterator_range<pred_iterator> {
+  return {pred_begin(), pred_end()};
+}
+
+//===----------------------------------------------------------------------===//
+// Successors
+//===----------------------------------------------------------------------===//
+
+/// This template implments the successor iterators for StmtBlock.
+template <typename BlockType>
+class StmtSuccessorIterator final
+    : public IndexedAccessorIterator<StmtSuccessorIterator<BlockType>,
+                                     BlockType, BlockType> {
+public:
+  /// Initializes the result iterator to the specified index.
+  StmtSuccessorIterator(BlockType *object, unsigned index)
+      : IndexedAccessorIterator<StmtSuccessorIterator<BlockType>, BlockType,
+                                BlockType>(object, index) {}
+
+  StmtSuccessorIterator(const StmtSuccessorIterator &other)
+      : StmtSuccessorIterator(other.object, other.index) {}
+
+  /// Support converting to the const variant. This will be a no-op for const
+  /// variant.
+  operator StmtSuccessorIterator<const BlockType>() const {
+    return StmtSuccessorIterator<const BlockType>(this->object, this->index);
+  }
+
+  BlockType *operator*() const {
+    return this->object->getSuccessor(this->index);
+  }
+
+  /// Get the successor number in the terminator.
+  unsigned getSuccessorIndex() const { return this->index; }
+};
+
+inline auto StmtBlock::succ_begin() const -> const_succ_iterator {
+  return const_succ_iterator(this, 0);
+}
+
+inline auto StmtBlock::succ_end() const -> const_succ_iterator {
+  return const_succ_iterator(this, getNumSuccessors());
+}
+
+inline auto StmtBlock::getSuccessors() const
+    -> llvm::iterator_range<const_succ_iterator> {
+  return {succ_begin(), succ_end()};
+}
+
+inline auto StmtBlock::succ_begin() -> succ_iterator {
+  return succ_iterator(this, 0);
+}
+
+inline auto StmtBlock::succ_end() -> succ_iterator {
+  return succ_iterator(this, getNumSuccessors());
+}
+
+inline auto StmtBlock::getSuccessors() -> llvm::iterator_range<succ_iterator> {
+  return {succ_begin(), succ_end()};
+}
+
 } //end namespace mlir
 #endif  // MLIR_IR_STMTBLOCK_H
diff --git a/mlir/lib/IR/AsmPrinter.cpp b/mlir/lib/IR/AsmPrinter.cpp
index 58f34af60f50..2de17563d932 100644
--- a/mlir/lib/IR/AsmPrinter.cpp
+++ b/mlir/lib/IR/AsmPrinter.cpp
@@ -1011,6 +1011,7 @@ protected:
             }
         // Otherwise number it normally.
         LLVM_FALLTHROUGH;
+      case SSAValueKind::BlockArgument:
       case SSAValueKind::InstResult:
       case SSAValueKind::StmtResult:
         // This is an uninteresting result, give it a boring number and be
@@ -1576,8 +1577,9 @@ void IntegerSet::print(raw_ostream &os) const {
 void SSAValue::print(raw_ostream &os) const {
   switch (getKind()) {
   case SSAValueKind::BBArgument:
+  case SSAValueKind::BlockArgument:
     // TODO: Improve this.
-    os << "<bb argument>\n";
+    os << "<block argument>\n";
     return;
   case SSAValueKind::InstResult:
     return getDefiningInst()->print(os);
diff --git a/mlir/lib/IR/SSAValue.cpp b/mlir/lib/IR/SSAValue.cpp
index 14fd4a459d3e..2179ba0fc11d 100644
--- a/mlir/lib/IR/SSAValue.cpp
+++ b/mlir/lib/IR/SSAValue.cpp
@@ -56,6 +56,8 @@ Function *SSAValue::getFunction() {
     return getDefiningInst()->getFunction();
   case SSAValueKind::MLFuncArgument:
     return cast<MLFuncArgument>(this)->getFunction();
+  case SSAValueKind::BlockArgument:
+    return cast<BlockArgument>(this)->getFunction();
   case SSAValueKind::StmtResult:
     return getDefiningStmt()->findFunction();
   case SSAValueKind::ForStmt:
@@ -113,3 +115,14 @@ CFGFunction *BBArgument::getFunction() {
 MLFunction *MLValue::getFunction() {
   return cast<MLFunction>(static_cast<SSAValue *>(this)->getFunction());
 }
+
+//===----------------------------------------------------------------------===//
+// BlockArgument implementation.
+//===----------------------------------------------------------------------===//
+
+/// Return the function that this argument is defined in.
+MLFunction *BlockArgument::getFunction() {
+  if (auto *owner = getOwner())
+    return owner->findFunction();
+  return nullptr;
+}
diff --git a/mlir/lib/IR/Statement.cpp b/mlir/lib/IR/Statement.cpp
index 0f7e90bec320..d4c26d5a7553 100644
--- a/mlir/lib/IR/Statement.cpp
+++ b/mlir/lib/IR/Statement.cpp
@@ -47,6 +47,11 @@ template <> unsigned StmtOperand::getOperandNumber() const {
   return this - &getOwner()->getStmtOperands()[0];
 }
 
+/// Return which operand this is in the operand list.
+template <> unsigned StmtBlockOperand::getOperandNumber() const {
+  return this - &getOwner()->getBlockOperands()[0];
+}
+
 //===----------------------------------------------------------------------===//
 // Statement
 //===----------------------------------------------------------------------===//
diff --git a/mlir/lib/IR/StmtBlock.cpp b/mlir/lib/IR/StmtBlock.cpp
index 898dd7bc337b..8ecb903d21d5 100644
--- a/mlir/lib/IR/StmtBlock.cpp
+++ b/mlir/lib/IR/StmtBlock.cpp
@@ -20,9 +20,11 @@
 #include "mlir/IR/Statements.h"
 using namespace mlir;
 
-//===----------------------------------------------------------------------===//
-// Statement block
-//===----------------------------------------------------------------------===//
+StmtBlock::~StmtBlock() {
+  clear();
+
+  llvm::DeleteContainerPointers(arguments);
+}
 
 Statement *StmtBlock::getContainingStmt() {
   switch (kind) {
@@ -62,3 +64,82 @@ StmtBlock::findAncestorStmtInBlock(const Statement &stmt) const {
   }
   return currStmt;
 }
+
+//===----------------------------------------------------------------------===//
+// Argument list management.
+//===----------------------------------------------------------------------===//
+
+BlockArgument *StmtBlock::addArgument(Type type) {
+  auto *arg = new BlockArgument(type, this);
+  arguments.push_back(arg);
+  return arg;
+}
+
+/// Add one argument to the argument list for each type specified in the list.
+auto StmtBlock::addArguments(ArrayRef<Type> types)
+    -> llvm::iterator_range<args_iterator> {
+  arguments.reserve(arguments.size() + types.size());
+  auto initialSize = arguments.size();
+  for (auto type : types) {
+    addArgument(type);
+  }
+  return {arguments.data() + initialSize, arguments.data() + arguments.size()};
+}
+
+void StmtBlock::eraseArgument(unsigned index) {
+  assert(index < arguments.size());
+
+  // Delete the argument.
+  delete arguments[index];
+  arguments.erase(arguments.begin() + index);
+
+  // Erase this argument from each of the predecessor's terminator.
+  for (auto predIt = pred_begin(), predE = pred_end(); predIt != predE;
+       ++predIt) {
+    auto *predTerminator = (*predIt)->getTerminator();
+    predTerminator->eraseSuccessorOperand(predIt.getSuccessorIndex(), index);
+  }
+}
+
+//===----------------------------------------------------------------------===//
+// Terminator management
+//===----------------------------------------------------------------------===//
+
+OperationStmt *StmtBlock::getTerminator() {
+  if (empty())
+    return nullptr;
+
+  // Check if the last instruction is a terminator.
+  auto &backInst = statements.back();
+  auto *opStmt = dyn_cast<OperationStmt>(&backInst);
+  if (!opStmt || !opStmt->isTerminator())
+    return nullptr;
+  return opStmt;
+}
+
+/// Return true if this block has no predecessors.
+bool StmtBlock::hasNoPredecessors() const { return pred_begin() == pred_end(); }
+
+// Indexed successor access.
+unsigned StmtBlock::getNumSuccessors() const {
+  return getTerminator()->getNumSuccessors();
+}
+
+StmtBlock *StmtBlock::getSuccessor(unsigned i) {
+  return getTerminator()->getSuccessor(i);
+}
+
+/// If this block has exactly one predecessor, return it.  Otherwise, return
+/// null.
+///
+/// Note that multiple edges from a single block (e.g. if you have a cond
+/// branch with the same block as the true/false destinations) is not
+/// considered to be a single predecessor.
+StmtBlock *StmtBlock::getSinglePredecessor() {
+  auto it = pred_begin();
+  if (it == pred_end())
+    return nullptr;
+  auto *firstPred = *it;
+  ++it;
+  return it == pred_end() ? firstPred : nullptr;
+}