Abstract: A key step in Yau's solution of the Calabi conjecture is the uniform L^infinity estimate for the complex Monge-Ampere equation on compact Kahler manifolds. New methods have been introduced by Kolodziej, Blocki, Szekelyhidi, and very recently Guo-Phong-Tong. In this talk, we introduce yet a new approach valid on compact hermitian manifolds. Quasi-plurisubharmonic envelopes play a vital role in our proof as well as our resolution of complex Monge-Ampere equations in several degenerate settings. Joint work with Vincent Guedj (IMT).