Most environmental processes involve variability over both space and time.
The extension of traditional geostatistical methods, such as kriging, to the spatio-temporal domain is one possible approach to characterize this variability. In this talk, I present this descriptive approach and an approach that uses a statistical model that is temporally dynamic and spatially descriptive. With the inclusion of a measurement equation, this formulation naturally leads to the development of a spatio-temporal Kalman filter. This can be viewed as empirical Bayesian inference in a hierarchical model. I then go on to discuss fully Bayesian inference for spatio-temporal data.