Particle systems exhibit various dynamics such as collision, interaction and collective motions that can lead to lots of applications in biology, physics and engineering. One major modelling strategy is to start with individual-based models that consists of ordinary differential equations describing the dynamics of each particle due to physical laws, and then derive the mean-field and fluid models in the mesoscopic and macroscopic levels. The models in different scales are suitable for certain applications of great interests. We will present the classic theory on the connection between particle models and McKean-Vlasov equations, and discuss the open questions.
