Abstract: Calabi conjectured that the complex Monge-Ampère equation on compact Kaehler manifolds has a unique solution. This was solved by Yau in 1978. In this talk, we present a non-archimedean version on projective Berkovich spaces. In joint work with Burgos, Jell, Künnemann and Martin, we improve a result of Boucksom, Favre and Jonsson in the equicharacteristic 0 case. We give also a result in positive equicharacteristic using test ideals.