During the last twenty five years the intersection cohomology of complex varieties has played an important role in representation theory. Usually one considers coefficients in characteristic 0, however recently the importance of positive characteristic coefficients has been realised. I will begin by trying to give an idea of intersection cohomology and why it is important in representation theory. I will then explain what is different in positive characteristic and give some examples of interesting behaviour in positive characteristic. Lastly I will explain joint work with Peter Fiebig determining the "p-smooth locus" of Schubert varieties in many cases.