||Since the pioneering work of Mess, one of the important tools for the study of globally hyperbolic anti-de Sitter manifolds is their resemblance with hyperbolic quasi-Fuchsian manifolds. One of the striking properties of quasi-Fuchsian manifolds is that their limit sets provide simple examples of fractals. It is known since the work of Patterson and Sullivan that their geometry is linked to asymptotic invariants of the hyperbolic manifolds. More precisely, the Hausdorff dimension of the limit set is equal to the critical exponent of the hyperbolic manifold. I will present a joint work with Olivier Glorieux (Luxembourg) in which we find an analogous description of the geometry of limit sets in anti-de Sitter geometry. We will discuss various asymptotic invariants of anti-de Sitter manifolds that can be linked to the geometry of these limit sets.