In this Chapter we provide a critical review of parametric and semiparametric spatial econometric approaches. We focus on the capability of each class of models to fit the main features of spatial data (such as strong and weak cross-sectional dependence, spatial heterogeneity, nonlinearities, and time persistence), leaving aside the technicalities related to the estimation methods. We also provide a brief discussion of the existent software developed to estimate most of the econometric models exposed in this Chapter.