The focus of the research is set on mathematical modeling of the electrical behavior of the human left ventricle. In order to achieve quantitative simulations in the scope of this focus new models are developed and existing models are enhanced. The designed anatomical and electrophysiological models are used to simulate and investigate the interplay for either physiological and pathological cases. The results help to gain new insights into the human cardiac functions not elaborated to date or to support the understanding of pathologies e.g. cardiac arrhythmias.