The His-Purkinje System (HPS) is responsible for the rapid electric conduction in the ventricles. It relays electrical impulses from the atrioventricular node to the muscle cells and, thus, coordinates the contraction of ventricles in order to ensure proper cardiac pump function. The HPS has been implicated in the genesis of ventricular tachycardia and fibrillation as a source of ectopic beats, as well as forming distinct portions of reentry circuitry. Despite its importance, it remains much less well characterized, structurally and functionally, than the myocardium. Notably, important differences exist with regard to cell structure and electrophysiology, including ion channels, intracellular calcium handling, and gap junctions. Very few computational models address the HPS, and the majority of organ level modeling studies omit it. This review will provide an overview of our current knowledge of structure and function (including electrophysiology) of the HPS. We will review the most recent advances in modeling of the system from the single cell to the organ level, with considerations for relevant interspecies distinctions.