Introduction -- An overview of model-based statistics -- Gaussian models for geostatistical data -- Generalized linear models for geostatistical data -- Classical parameter estimation -- Spatial prediction -- Bayesian inference -- Geostatistical design -- A statistical background. This volume is the first book-length treatment of model-based geostatistics. The text is expository, emphasizing statistical methods and applications rather than the underlying mathematical theory. Analyses of datasets from a range of scientific contexts feature prominently, and simulations are used to illustrate theoretical results. Readers can reproduce most of the computational results in the book by using the authors' software package, geoR, whose usage is illustrated in a computation section at the end of each chapter. The book assumes a working knowledge of classical and Bayesian methods of inference, linear models, and generalized linear models.