This thesis describes the development of biophysically detailed computer models of the human atria and torso to study the underlying mechanisms of cardiac diseases, some of the most common causes of morbidity and mortality. This is a cross-disciplinary project, involving fundamentals of cardiac electrophysiology, physics of excitable media, applied mathematics and high performance scientific computing and visualisation. The author uses computer models to provide insights into the underlying mechanisms of the genesis of atrial fibrillation and develops novel techniques for the monitoring of atrial tachycardia.