The Enriques classification of algebraic surfaces was a milestone in the development of algebraic geometry and serves as inspiration for the birational classification of higher dimensional varieties pursued currently. I will discuss new phenomena that do not occur in the case of curves and introduce some crucial tools before presenting the classification according to the Kodaira dimension and birational invariants. I will present a proof using modern ideas from Mori’s minimal model program, which extends to the dimension > 2 case.