Abstract: We are interested in convex lattice polytopes, that is, convex polytopes whose vertices have integer coordinates.  Typically, one can ask combinatorial questions (how many polytopes of this kind are contained in a big cube ?) or probabilistic questions (how does a random polytope of this kind contained in a big cube look like ?). In dimension 3 or higher, these questions remain essentially open. We present some probabilistic results in dimension 2 and in dimension 3 for a subclass of polytopes called zonotopes.