An endomorphism f of a normal projective variety X is polarized if the pullback via f of an ample divisor H is linearly equivalent to qH for some q>1. Non-trivial endomorphisms on projective spaces or multiplication maps on Abelian varieties are examples of such maps. We show that for mildly singular X, we can run an f-equivariant minimal model program. As a result, the building blocks of polarized endomorphisms are those on Fano varieties of Picard number one and those on Abelian varieties (or their quasi-etale quotients). In particular, we show that (a power of) every polarized endomorphism of a smooth rationally connected variety acts as a scalar on the Neron-Severi group. This is a joint work with S. Meng. Speaker(s): De-Qi Zhang (National University of Singapore)