A view on contractions of higher dimensional varieties

In this paper we discuss some recent results about extremal contractions of complex algebraic varieties. These are proper surjective maps, $\phi: X\longrightarrow Z$, of normal varieties with connected fibers such that $X$ has mild singularities (in particular $X$ is $Q$-Gorenstein) and the anticanonical divisor of $X$ is $\phi$ ample. It will appear on the Proceedings of AMS-SRI on Algebraic Geometry, Santa Cruz 1995.