Different models of computation have been introduced in Computer Science. Some of these models involve the use of probabilities, and also "nondeterminism", that arises when one considers the interaction of processes running in parallel. One of the main concerns is to find appropriate definitions for the intuitive concept of "equivalence of behavior" for processes. A formal version of this notion is given by bisimilarity, the study of which gives rise to a few problems with a descriptive-set-theoretical flavor. In this talk I'll survey some of these problems.