In this thesis, we study the long-range behaviour of polymerized membranes using a non-perturbative renormalization group (NPRG) approach. We start by presenting the NPRG after which we introduce membrane systems. In our work, we concentrate on polymerized membranes of different types: homogeneous, anisotropic and quenched disordered. Moreover as a side project, we work on Lifshitz critical behaviour (LCB) in magnetic systems. Our results, both for polymerized membranes and LCB, compare well with weak-coupling, low-temperature and large-d (or large-n for LCB) perturbative results in the limiting cases. But more importantly the need of a non-perturbative approach is justified by the fact that the physically interesting cases have been difficult to compute. A long-standing question in homogeneous membranes is the order of the transition between the crumpled and flat phases. Although we do not have a definite answer, our results seem to indicate that the transition is first order in agreement with recent Monte Carlo simulations. An interesting feature of homogeneous membranes is the existence of the flat phase at low-temperature with a non-trivial behaviour. This flat phase has shown to correctly describe the behaviour of graphene although the electronic degrees of freedom are not taken into account
