Introduction. A review of spatiotemporal statistics. Science-based vs. data-processing statistics. Space-time metrics: Euclidean (spatially isotropic and non-isotropic). Non-Euclidean (river network, gravity model, isomap). Spatiotemporal random field theory (S/TRF): Ordinary S/TRF. Generalized S/TRF. Spatiotemporal statistics of data sets. Standard two-point statistics: Ordinary covariance and variogram. Generalized covariance and variogram. Extension to multi-point statistics. Spatiotemporal exploratory analysis (pattern recognition). Empirical orthogonal method: Atmospheric and hydrological applications. Dynamic factor analysis: Ecological and environmental applications. Spatiotemporal clustering analysis: SaTscan and other works. Spatiotemporal statistics of differential equations. The analytical approach: Closed form expressions of physical and biophysical laws. Low- and high-order (diagrammatic) approximations of groundwater flow. The numerical approach: First order second moment (FOSM) method. Adjoint method. Spatiotemporal trend analysis. Non-parametric approaches. The generalized additive model. The Kernel smoothing method. Spatiotemporal regression.