We recap the notion of dominance from LLVM, and provide an overview of how this has been transplanted to MLIR. The notion of dominance is complicated in the presence of regions: The control flow across regions and basic blocks is under-specified. MLIR has control flow interfaces to model control flow and dominance. However, key properties of LLVM dominance (e.g. if A dominates B, then variables live in A continue to be live in B) need not be true in MLIR. We provide such examples of under-specification in MLIR, and propose potential ways forward that warrant discussion.