  We make a systematic study of (quasi-)plurisubharmonic envelopes on compact
K\"ahler manifolds, as well as on domains of $\mathbb{C}^n$, by using and
extending an approximation process due to Berman [Ber13]. We show that the
quasi-psh envelope of a viscosity super-solution is a pluripotential
super-solution of a given complex Monge-Amp\`ere equation. We use these ideas
to solve complex Monge-Amp\`ere equations by taking lower envelopes of
super-solutions.
