This article investigates the modeling of a new type of degradation data: spatio-temporal degradation data collected from a spatial domain over time. Like existing stochastic degradation models, a random field is constructed to describe the spatio-temporal degradation process. We model the degradation process as an additive superposition of two stochastic components: a dynamic spatial degradation generation process and a spatio-temporal propagation process. Some common challenges are addressed, including the spatial heterogeneity of the degradation process, spatial propagation of degradation to neighboring areas, anisotropic and space-time non-separable covariance structures associated with a complex spatio-temporal degradation process, and the computational issues related to parameter estimation and simulation. When spatial dependence is ignored, we show that the proposed spatio-temporal degradation model incorporates some existing purely time-dependent degradation models as its special cases. We also show the connection, under special conditions, between the proposed statistical model and a class of physical-degradation processes given by stochastic partial differential equations. Numerical examples are presented to illustrate modeling approach, parameter estimation, model validation, and applications.