The literature on probabilistic hazard and risk assessment shows a rich and wide variety of modeling strategies tailored to specific perils. On one hand, catastrophe (CAT) modeling, a recent professional and scientific discipline, provides a general structure for the quantification of natural (e.g., geological, hydrological, meteorological) and man-made (e.g., terrorist, cyber) catastrophes. On the other hand, peril characteristics and related processes have yet to be categorized and harmonized to enable adequate comparison, limit silo effects, and simplify the implementation of emerging risks. We reviewed the literature for more than 20 perils from the natural, technological, and socio-economic systems to categorize them by following the CAT modeling hazard pipeline: (1) event source → (2) size distribution → (3) intensity footprint. We defined the following categorizations, which are applicable to any type of peril, specifically: (1) point/line/area/track/diffuse source, (2) discrete event/continuous flow, and (3) spatial diffusion (static)/threshold (passive)/sustained propagation (dynamic). We then harmonized the various hazard processes using energy as the common metric, noting that the hazard pipeline’s underlying physical process consists of some energy being transferred from an energy stock (the source), via an event, to the environment (the footprint).