diff --git a/mlir/lib/Target/LLVMIR/ConvertFromLLVMIR.cpp b/mlir/lib/Target/LLVMIR/ConvertFromLLVMIR.cpp
--- a/mlir/lib/Target/LLVMIR/ConvertFromLLVMIR.cpp
+++ b/mlir/lib/Target/LLVMIR/ConvertFromLLVMIR.cpp
@@ -498,6 +498,42 @@
       return nullptr;
     return instMap[c] = bEntry.create<UndefOp>(UnknownLoc::get(context), type);
   }
+
+  if (isa<llvm::ConstantAggregate>(c) || isa<llvm::ConstantAggregateZero>(c)) {
+    unsigned numElements = c->getNumOperands();
+    std::function<llvm::Constant *(unsigned)> getElement =
+        [&](unsigned index) -> llvm::Constant * {
+      return c->getAggregateElement(index);
+    };
+    // llvm::ConstantAggregateZero doesn't take any operand
+    // so its getNumOperands is always zero.
+    if (auto *caz = dyn_cast<llvm::ConstantAggregateZero>(c)) {
+      numElements = caz->getElementCount().getFixedValue();
+      // We want to capture the pointer rather than reference
+      // to the pointer since the latter will become dangling upon
+      // exiting the scope.
+      getElement = [=](unsigned index) -> llvm::Constant * {
+        return caz->getElementValue(index);
+      };
+    }
+
+    // Generate a llvm.undef as the root value first.
+    Type rootType = processType(c->getType());
+    if (!rootType)
+      return nullptr;
+    Value root = bEntry.create<UndefOp>(unknownLoc, rootType);
+    for (unsigned i = 0; i < numElements; ++i) {
+      llvm::Constant *element = getElement(i);
+      Value elementValue = processConstant(element);
+      if (!elementValue)
+        return nullptr;
+      ArrayAttr indexAttr = bEntry.getI32ArrayAttr({static_cast<int32_t>(i)});
+      root = bEntry.create<InsertValueOp>(UnknownLoc::get(context), rootType,
+                                          root, elementValue, indexAttr);
+    }
+    return root;
+  }
+
   emitError(unknownLoc) << "unhandled constant: " << diag(*c);
   return nullptr;
 }
diff --git a/mlir/test/Target/LLVMIR/import.ll b/mlir/test/Target/LLVMIR/Import/basic.ll
rename from mlir/test/Target/LLVMIR/import.ll
rename to mlir/test/Target/LLVMIR/Import/basic.ll
diff --git a/mlir/test/Target/LLVMIR/Import/constant-aggregate.ll b/mlir/test/Target/LLVMIR/Import/constant-aggregate.ll
new file mode 100644
--- /dev/null
+++ b/mlir/test/Target/LLVMIR/Import/constant-aggregate.ll
@@ -0,0 +1,32 @@
+; RUN: mlir-translate --import-llvm %s | FileCheck %s
+
+; CHECK-DAG: %[[C0:.+]] = llvm.mlir.constant(7 : i32) : i32
+; CHECK-DAG: %[[C1:.+]] = llvm.mlir.constant(8 : i16) : i16
+; CHECK-DAG: %[[C2:.+]] = llvm.mlir.constant(4 : i8) : i8
+; CHECK-DAG: %[[C3:.+]] = llvm.mlir.constant(9 : i32) : i32
+; CHECK: %[[ROOT:.+]] = llvm.mlir.undef : !llvm.struct<"SimpleAggType", (i32, i8, i16, i32)>
+; CHECK: %[[CHAIN0:.+]] = llvm.insertvalue %[[C3]], %[[ROOT]][0 : i32]
+; CHECK: %[[CHAIN1:.+]] = llvm.insertvalue %[[C2]], %[[CHAIN0]][1 : i32]
+; CHECK: %[[CHAIN2:.+]] = llvm.insertvalue %[[C1]], %[[CHAIN1]][2 : i32]
+; CHECK: %[[CHAIN3:.+]] = llvm.insertvalue %[[C0]], %[[CHAIN2]][3 : i32]
+; CHECK: llvm.return %[[CHAIN3]]
+%SimpleAggType = type {i32, i8, i16, i32}
+@simpleAgg = global %SimpleAggType {i32 9, i8 4, i16 8, i32 7}
+
+; CHECK: %[[NP:.+]] = llvm.mlir.null : !llvm.ptr<struct<"SimpleAggType", (i32, i8, i16, i32)>>
+; CHECK-DAG: %[[C0:.+]] = llvm.mlir.constant(4 : i32) : i32
+; CHECK-DAG: %[[C1:.+]] = llvm.mlir.constant(3 : i16) : i16
+; CHECK-DAG: %[[C2:.+]] = llvm.mlir.constant(2 : i8) : i8
+; CHECK-DAG: %[[C3:.+]] = llvm.mlir.constant(1 : i32) : i32
+; CHECK: %[[ROOT:.+]] = llvm.mlir.undef : !llvm.struct<"SimpleAggType", (i32, i8, i16, i32)>
+; CHECK: %[[CHAIN0:.+]] = llvm.insertvalue %[[C3]], %[[ROOT]][0 : i32]
+; CHECK: %[[CHAIN1:.+]] = llvm.insertvalue %[[C2]], %[[CHAIN0]][1 : i32]
+; CHECK: %[[CHAIN2:.+]] = llvm.insertvalue %[[C1]], %[[CHAIN1]][2 : i32]
+; CHECK: %[[CHAIN3:.+]] = llvm.insertvalue %[[C0]], %[[CHAIN2]][3 : i32]
+; CHECK: %[[ROOT2:.+]] = llvm.mlir.undef : !llvm.struct<"NestedAggType", (struct<"SimpleAggType", (i32, i8, i16, i32)>, ptr<struct<"SimpleAggType", (i32, i8, i16, i32)>>)>
+; CHECK: %[[CHAIN4:.+]] = llvm.insertvalue %[[CHAIN3]], %[[ROOT2]][0 : i32]
+; CHECK: %[[CHAIN5:.+]] = llvm.insertvalue %[[NP]], %[[CHAIN4]][1 : i32]
+; CHECK: llvm.return %[[CHAIN5]]
+%NestedAggType = type {%SimpleAggType, %SimpleAggType*}
+@nestedAgg = global %NestedAggType { %SimpleAggType{i32 1, i8 2, i16 3, i32 4}, %SimpleAggType* null }
+
diff --git a/mlir/test/Target/LLVMIR/data-layout.ll b/mlir/test/Target/LLVMIR/Import/data-layout.ll
rename from mlir/test/Target/LLVMIR/data-layout.ll
rename to mlir/test/Target/LLVMIR/Import/data-layout.ll
diff --git a/mlir/test/Target/LLVMIR/import-opaque.ll b/mlir/test/Target/LLVMIR/Import/opaque.ll
rename from mlir/test/Target/LLVMIR/import-opaque.ll
rename to mlir/test/Target/LLVMIR/Import/opaque.ll
diff --git a/mlir/test/Target/LLVMIR/Import/zeroinitializer.ll b/mlir/test/Target/LLVMIR/Import/zeroinitializer.ll
new file mode 100644
--- /dev/null
+++ b/mlir/test/Target/LLVMIR/Import/zeroinitializer.ll
@@ -0,0 +1,14 @@
+; RUN: mlir-translate --import-llvm %s | FileCheck %s
+
+%Domain = type { %Domain**, %Domain* }
+
+; CHECK: llvm.mlir.global external @D() :
+; CHECK-SAME: !llvm.struct<"Domain", (ptr<ptr<struct<"Domain">>>, ptr<struct<"Domain">>)> 
+; CHECK-DAG: %[[E0:.+]] = llvm.mlir.null : !llvm.ptr<struct<"Domain", (ptr<ptr<struct<"Domain">>>, ptr<struct<"Domain">>)>>
+; CHECK-DAG: %[[E1:.+]] = llvm.mlir.null : !llvm.ptr<ptr<struct<"Domain", (ptr<ptr<struct<"Domain">>>, ptr<struct<"Domain">>)>>>
+; CHECK: %[[ROOT:.+]] = llvm.mlir.undef : !llvm.struct<"Domain", (ptr<ptr<struct<"Domain">>>, ptr<struct<"Domain">>)>
+; CHECK: %[[CHAIN:.+]] = llvm.insertvalue %[[E1]], %[[ROOT]][0 : i32]
+; CHECK: %[[RES:.+]] = llvm.insertvalue %[[E0]], %[[CHAIN]][1 : i32]
+; CHECK: llvm.return %[[RES]]
+@D = global %Domain zeroinitializer
+