A natural problem in the computational treatment of finite matrix groups is the recognition of simple groups. That is, given a matrix group G known to be quasi-simple, determine the isomorphism type of G. If G is known to be of Lie type in given characteristic p, Babai, Kantor, Palfy and Serres describe an algorithm to solve this recognition problem. We report about an implementation of this (joint work with Eamonn O'Brien) as well as on an approach to guess the right characteristic p.