We review some recent results on the dynamics of holomorphic maps(or even meromorphic transforms )in several complex variables. We focus on the construction of measures of maximal entropy and their statistical properties(mixing,exponential decay of correlations). We will explain the method in two technically simple cases:polynomial like mappings and horizontal like mappings. The basic tools are:appropriate spaces of test forms adapted to complex dynamics,resolution of the ddc equation with good estimates,intersection of positive closed currents of any bidegree. This is joint work with T.C.Dinh