This thesis is about simulations of two classes of stochastic processes: Lévy processes and max-stable processes. The aim of a simulation is to find an algorithm that computes the possible values of a realization of a stochastic process X onto a finite number n of points. This means that the outcome of a sampling algorithm is a random vector that we would like to be representative of the whole process. In particular. we would like the random vector our simulation)to inherit the statistical properties of X. Then, the most ambitious goal that the simulation has the same distribution of the restriction of the stochastic process X onto the evaluation points.