The study of quotients by reductive groups is an important topic in algebraic geometry. It manifests when studying moduli spaces, orbit spaces, and G-varieties. Many important classes of singularities, as normal singularities and rational singularities, are preserved under quotients by reductive groups. In this talk, we will show that the singularities of the MMP are preserved under reductive quotients. The singularities of the MMP are a local version of Fano varieties. As an application, we show that projective moduli spaces of semistable quiver representations are of Fano type, in particular, Mori dream spaces.