Death due to lethal cardiac arrhythmias is the leading cause of mortality in Western society. Many of the fundamental mechanisms underlying the onset of arrthythmias, their maintenance and termination, still remain poorly understood. The specialized conduction (or His-Purkinje) system is fundamental to ventricular electrophysiological function and is a key player in various cardiac diseases. In recent years, computational simulation has become an important tool in im- proving our understanding ofthese mechanisms. Current state-of-the-art computational ventric- ular electrophysiology models often do not feature a detailed representation of the specialized conduction system. Ventricular models that do incorporate the specialized conduction system often use a simplified anatomical description and are commonly based on the monodomain equations, rather than the more general bidomain equations. Thus, using computational simula- tion to investigate both normal physiological function of the specialized conduction system and pathologies in which it is involved presents difficulties. This thesis develops the techniques and tools required to model the specialized conduction sys- tem at the ventricular scale. We derive one-dimensional bidomain equations that model elec- trical propagation in the system by reducing the equations associated with a three-dimensional fibre. To complement the derived equations, we develop a numerical solution scheme for the model that is efficient enough to allow ventricular simulations. The one-dimensional bido- main model allows defibrillation studies to be performed with the specialized conduction sys- tem. Secondly, we investigate the imaging and mesh generation tools required to integrate an anatomically detailed mesh of the specialized conduction system into a current state-of-the-art ventricular mesh. Using these tools, a highly detailed rabbit-specific specialized conduction system anatomical model is developed. Simulations are performed that dem~strate the re- sponse of the specialized conduction system to defibrillation strength shocks and we compare activation sequences generated using the model to experimental recordings. Finally, we investi- gate variability in the anatomy of the system. The tools and ventricular model presented in this thesis fulfil an important role in allowing the study of the e1ectrophysiological function of the specialized conduction system at the ventricular scale.