Abstract　 　　
　 Debris discs have been observed around an important fraction of main sequence stars. Most of them have been detected by the Infra-Red excess luminosity due to the presence of dust grains, but some of them have also been imaged on resolved images (from the visible to millimetre wavelengths). These discs are believed to be made of remnants from the planet-formation process that have not been incorporated into planets, and are thus similar to the asteroid and Kuiper belts from our own solar system. Debris discs provide us with a unique opportunity to understand "what is going on" in planetary systems, because they are often the most easily detectable part of such systems. As such, their mass, their composition and their spatial structure are essential clues to obtain a global picture of a given system. However, studying debris discs is not an straightforward task, because we only see the smallest grains that they are made of. These grains are produced by a collisional cascade going up to much larger bodies that are undetectable to observations. The challenge is thus to reconstruct the whole disc from this limited observational information. Given the complexity of the processes at play in debris discs, such as destructive collisions, gravitational perturbations or stellar radiation pressure, sophisticated numerical models have to be used. I will review the main models that are commonly used to study these discs, that is, statistical models studying their global collisional evolution, and N-body codes to study their dynamical evolution. I will also focus on the latest generation of models, in part developed by our French team, that for the first time are able to combine these 2 types of codes into one global self-consistent code.