Algebraic varieties are geometric objects defined by polynomial equations. The minimal model program (MMP) is an ambitious program that aims to classify algebraic varieties. According to the MMP, there are 3 building blocks: Fano varieties, Calabi-Yau varieties and varieties of general type which are higher dimensional analogs of Riemann Surfaces of genus 0,1 or at least 2 respectively. In this talk I will recall the general features of the MMP and discuss recent advances in our understanding of Fano varieties and varieties of general type.