Consider a system of N interacting particles evolving over time with Markovian dynamics. The interaction occurs only due to a shared resource. I shall briefly sketch the classical tightness-existence-uniqueness approach used to prove weak convergence of the system to a limiting system as N tends to infinity. I shall illustrate another approach in more detail with the example of a nonlinear Markov chain. In the case of exchangeable particles, weak convergence of the system implies propogation of chaos i.e, in the limiting system particles evolve independently due to a deterministically shared resource.