Spatial autocorrelation models are critical tools in the analysis of spatial environmental, epidemiological, and ecological data. While the most common spatial models, such as Matern or CAR models, have well-established utility for prediction and smoothing, the interpretation of standard spatial models is rarely straightforward. We first consider the Rubin causal model applied to spatial statistics, and illustrate how standard spatial models are unable to directly answer causal questions that are of interest in common situations. We then present a general class of spatial models that directly model scientific mechanisms underlying common processes in environmental health and ecology. This class of models contains common Matern, CAR, and SAR models as special cases, and allows for causal modeling of spatial data in scenarios where the scientific mechanism underlying spatial autocorrelation is well-understood.