After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (e.g. the solution set of a system of polynomial equations defined by p1,...,prp1,...,pr in C[x1,...,xn]C[x1,...,xn]) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic p>0p>0. Many technical difficulties arise in this context. Nevertheless, there has been much progress recently. In particular, the MMP was established for 3-folds in characteristic p>5p>5 by work of Birkar, Hacon, Xu and others. In this talk, we will explain some of the challenges and the recent progress in this active area of research.