We will discuss the dynamics of set-valued functions and talk about some basic facts of these systems. In 2015, [Carrasco, Metzger and Morales] introduced two kinds of entropy, that they call separated and spanning entropy, given by separated and spanning sets respectively. In the same year, [Kelly and Tennant] introduced a notion of entropy that resemble the classical notion of topological entropy of single-valued maps, and show that the entropy of a set-valued function is equal to the topological entropy of the shift map on its orbit spaces. We will talk about the differences of these definitions of topological entropy for set valued funtions. This is joint work with MJ Pacifico.