abstract: After introducing some basic notions and examples, e.g. Hénon maps on Ck and positive closed currents, I will discuss some fundamental problems in pluripotential theory with several applications in complex dynamics. I will talk about (1) the regularization of positive closed currents, dynamical degrees and entropy, (2) the theory of super-potentials and ergodicity, (3) the theory of density of currents and equidistribution of periodic points. The talk is based on my joint works with N. Sibony and V.A. Nguyen.