Algebraic geometry is the study of geometric objects defined as the solution set of a system of polynomial equations $p_1,\ldots , p_r\in F[x_1,\ldots , x_n]$ where $F$ is an algebraically closed field. After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (eg. $F=\mathbb C$) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic $p>0$. Despite numerous technical difficulties there has been some interesting recent progress in this direction. In particular the MMP was established for 3-folds in characteristic $p>3$ by work of Birkar, Hacon, Witaszek, Xu and others. In this talk, we will explain some of the challenges and the recent progress in this active area of research.