In recent years, interest has grown in modeling spatio-temporal data generated from
monitoring networks, satellite imaging, and climate models. Under Gaussianity, the
covariance function is core to spatio-temporal modeling, inference, and prediction. In this
article, we review the various space-time covariance structures in which simplified
assumptions, such as separability and full symmetry, are made to facilitate computation, and
associated tests intended to validate these structures. We also review recent developments …