Smale spaces are a class of dynamical system defined by Ruelle to axiomatize properties of basic sets of an Axiom A diffeomorphism. From a Smale space one can construct a number of C*-algebras; each is obtained from an equivalence relation. When the original system is mixing each of these C*-algebras is simple, separable, nuclear, and stably finite. I will discuss recent results on the structure of these algebras along with group actions on them. This talk is based on joint work with Karen Strung and Allan Yashinski.