  Toric geometry provides a bridge between algebraic geometry and combinatorics
of fans and polytopes. For each polarized toric variety (X,L) we have
associated a polytope P. In this thesis we use this correspondence to study
birational geometry for toric varieties. To this end, we address subjects such
as Minimal Model Program, Mori fiber spaces, and chamber structures on the cone
of effective divisors. We translate some results from these theories to the
combinatorics of polytopes and use them to get structure theorems on space of
polytopes. In particular, we treat toric varieties known as 2-Fano, and we
classify them in low dimensions.
