Algebraic curves were essentially classified around the time of Riemann (mid-19th century). The classification of algebraic surfaces was largely completed by the Italian geometers (Castelnuovo, Enriques, Segre, Severi...) at the end of the 19th century. The goal of the (Mori) Minimal Model Programme is to bring some order to higher dimensional algebraic geometry by generalizing some of the features of the classification results for curves and surfaces. In this talk I will describe some of the main ideas, such as the role of the canonical bundle and rational curves.