The notion of cluster tilting plays an important role in representation theory. In this talk I will discuss cluster tilting modules in the category of maximal Cohen-Macaulay modules. Their basic properties as well as some examples will be explained. In particular extending a result in\ Reiten's lecture, we give a generalization of Auslander's algebraic McKay correspondence between stable categories of maximal Cohen-Macaulay modules and generalized cluster categories (joint work with Amiot, Reiten).