As shown in Chapter 2, estimation of spatial models via least squares can lead to inconsistent estimates of the regression parameters for models with spatially lagged dependent variables, inconsistent estimation of the spatial parameters, and inconsistent estimation of standard errors. In contrast, maximum likelihood is consistent for these models (Lee, 2004). Consequently, this chapter focuses on maximum likelihood estimation of spatial regression models. Historically, much of the spatial econometrics literature has focused on ways to avoid maximum likelihood estimation because of perceived computational difficulties. There have been a great many improvements in computational methods for maximum likelihood estimation of spatial regression models since the time of Anselin’s 1988 text. These improvements allow models involving samples containing more than 60,000 US Census tract observations to be estimated in only a few seconds on desktop and laptop computers.