We present the MLIR `ValueBoundsConstraintSet` infrastructure, which can compute lower/upper/equality bounds of index-typed SSA values or dynamic dimension sizes of shaped values, in terms of other SSA values or as a constant. For example, this infrastructure has been used to enable vectorization of tensor IR with dynamic dimension sizes and to hoist dynamic memory allocations from loops. In this talk, we present the infrastructure's API, how to extend it with custom ops and touch upon current limitations.