Large systems of interacting particles are very complex but also interplay with a large set of applications, from cosmology to the biosciences. Particles can actually represent a wide range of objects: galaxies in some cosmological models, ions or electrons in plasmas, bacteria or cells in biosciences, ``agents'' in economics or social sciences. A classical way of reducing the complexity of those large systems is through the derivation of appropriate limit equations, in particular with the so-called mean field limits. We will introduce and explain some classical and more recent results on the mean field limit and propagation of chaos for systems of many particles, leading to Vlasov, McKean-Vlasov or macroscopic equations.