The development of diagnostics to check the fit of a proposed Markov random field (MRP) to data is a very important problem in spatial statistics. In this article, the consequences of fitting a given MRF to spatial data are visualized using diagnostic plots. The Gaussian MRF known as the conditional autoregressive model is featured. Various types of departures of the data from the fitted MRF model are calculated, allowing locally influential observations to be highlighted using the MRF-Neighborhoods plot. Through a global summary statistic and the Model-Comparison plot, we compare MRF models that differ both in terms of the neighborhood structure and the parameterization of spatial dependence. © 2008 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.