The notion of propagation of chaos for large systems of interacting
particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old
and new methods as well as several important results in the field. The models
considered include the McKean-Vlasov diffusion, the mean-field jump models
and the Boltzmann models. The first part of this review is an introduction
to modelling aspects of stochastic particle systems and to the notion of propagation of chaos. The second part presents concrete applications and a more
detailed study of some of the important models in the field.