Summary Various diagnostics for generalized linear models are reviewed and extended to more general models. These include some models for censored and grouped data, and regressions that are nonlinear, or where the response does not have an exponential family distribution. Among diagnostics considered are score tests, various types of residual, and approximate Cook statistics. Diagnostics for models with incidental parameters orthogonal to the regression parameters are discussed. Examples are given and the adequacy of approximations is considered.