  The scientific rigor and computational methods of causal inference have had
great impacts on many disciplines, but have only recently begun to take hold in
spatial applications. Spatial casual inference poses analytic challenges due to
complex correlation structures and interference between the treatment at one
location and the outcomes at others. In this paper, we review the current
literature on spatial causal inference and identify areas of future work. We
first discuss methods that exploit spatial structure to account for unmeasured
confounding variables. We then discuss causal analysis in the presence of
spatial interference including several common assumptions used to reduce the
complexity of the interference patterns under consideration. These methods are
extended to the spatiotemporal case where we compare and contrast the potential
outcomes framework with Granger causality, and to geostatistical analyses
involving spatial random fields of treatments and responses. The methods are
introduced in the context of observational environmental and epidemiological
studies, and are compared using both a simulation study and analysis of the
effect of ambient air pollution on COVID-19 mortality rate. Code to implement
many of the methods using the popular Bayesian software OpenBUGS is provided.
