General methods for assessing model fit are motivated, and are applied to network data, with modifications appropriate to the network context. For instance, plots such as the QQ-plot can be used to give a graphical idea of how well the distribution of a statistic matches its theoretical (perhaps simulated) distribution. As an example, the empirical distribution of the degrees in a Bernoulli random graph can be compared to the distribution function of their theoretical binomial distribution; although such a fit typically looks good, there is actually a difference between the two that is detectable by repeating the experiment often enough, because of the dependence between the degrees. Fit can also be judged by using generalized likelihood ratio tests, and pure significance tests such as Pearson’s statistic. When a model is not available, it may still be possible to justify Monte Carlo tests. Goodness of fit is considered in particular in the context of Bernoulli and Erdős–Rényi mixture models, the GPDS model and exponential random graph models.