In most network models, the distributions of summary statistics are rarely known exactly. However, it may well be possible to approximate their distributions by other, well-known distributions, when the values of local statistics at different vertices are only weakly dependent. Such settings are well suited to the application of the Stein–Chen method, which, in the context of Poisson approximation, enables concrete estimates of the approximation error to be derived, with respect to the total variation distance. In this chapter, the Stein–Chen method is developed in some detail. A Stein equation is derived, together with the necessary properties of its solutions, and a general estimate of approximation error is given, which is expressed solely in terms of the random variable whose distribution is being approximated. The method is applied to sums of dependent random variables, using both a local and a coupling approach. Examples given include the number of triangles and the number of isolated vertices in a Bernoulli random graph.