Spatial-temporal point processes have been useful for applications in many fields, including the study of earthquakes, wildfires, and other natural disasters, as well as forests and other ecological data, neurological data, invasive species, epidemics, spatial debris, and many others. Recent works draw new conclusions about the general model, applications to earthquakes, higher-order statistics, or residual analysis. Within each chapter of the thesis, the principles from published articles are summarized. Various sorts of spatial-temporal point processes, models, and solution are reviewed under the general model heading. The section on earthquakes traces longitudinal developments in one area of application. Expectations for behavior in spatial-temporal distributions are expanded upon in the chapter on higher-order statistics. Residuals in the spatial-temporal domain conclude the analysis.