Regression analysis is the term used to describe a family of methods that seek to model the relationship between one (or more) dependent or response variables and a number of independent or predictor variables. Spatial regression methods are similar, but take explicit account of the spatial structure of data, in particular the lack of independence that typically exists between measurements made at nearby locations. Initially we describe the basic models applied in ordinary regression and the application of this kind of technique to trend surface analysis. We then examine three different approaches to addressing the complexities that arise when attempting to model spatial datasets using regression techniques. The first of these involves varying the model parameters spatially using a technique known as Geographically Weighted regression (GWR). The second seeks to analyze the pattern and degree to which the sampled data are spatially correlated (or autocorrelated), and to use this information in order to construct regression models that recognize this structure and include it within their designs. The third approach attempts to apply simple filters or differencing to the data to remove the spatial variation and then model the filtered data.