Beginning with the simple derivation of the (deterministic) law of mass action from Markov chain models of chemical reaction networks, we will illustrate the derivation of deterministic, piecewise deterministic, and stochastically perturbed deterministic models from increasingly complex stochastic models. The arguments exploit asymptotic properties of stochastic equations and limits of exchangeable systems. The last method will be applied to obtain results of Robert and Touboul for a neural network model.