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.