This chapter lays the theoretical foundations for the approach to spatio-temporal modeling from data typically found in conflict data sets. The chapter begins by outlining the basic principles of point-process theory, starting from the definition of the Poisson distribution and ending with a description of the log-Gaussian Cox process and the point-process likelihood function. The chapter proceeds to discuss two important classes of spatio-temporal models, the stochastic partial differential equation (SPDE) and the stochastic integro-difference equation (SIDE). Dimensionality reduction techniques to reduce these models into state-space form are then given. Recrusive estimation algorithms for estimation with a state-space model are then derived and are followed by a strategy to include unknown parameters within the estimation framework through variational Bayes. The chapter concludes with a section on implementation tools. This includes details on non-parametric methods for obtaining descriptive statistics from events, a basis function placement method and a variational-Laplace algorithm for inference under the point-process likelihood.