The classical Rokhlin lemma states that an aperiodic measure preserving dynamical system can be decomposed to an arbitrary high tower of measurable sets and a remainder of arbitrarily small measure. Then let us say that a topological dynamical system has the uniform Rokhlin property if it can be decomposed to arbitrary high towers of open sets and a remainder which is uniformly small with respect to all invariant probability measures. Any free and minimal Z^n action have the uniform Rokhlin property. In the talk, I’ll discuss the applications of the uniform Rokhlin property to the structure of the crossed product C*-algebras such as comparison radius, stable rank, and Jiang-Su stability, and I’ll also talk about a recent application to the Roe algebra of a discrete amenable group.