Despite the overwhelming wealth of biological data available today, gaining mechanistic insight into cardiac function remains to be a challenging endeavor. In no small part, this is due to the multiscale/multiphysics nature of cardiac function, which is governed by complex interactions of processes, arising within and across levels of biological organization, as well as between electrical, mechanical and fluidic systems. Considering the prevalence of cardiac disease, a better understanding of the underlying physical mechanisms is of pivotal importance. Computer models are considered among the most promising approach for gaining better insight into cardiac function as they provide a powerful quantitative framework for the integration of experimental data and allow for a careful analysis of complex cause-effect relationship across different spatial scales and physics. Owing to recent advances in medical imaging, refined experimental and numerical techniques in silico models became extremely highdimensional to capture both anatomical structure and physiological function at a high level of detail. Such high dimensional models impose significant computational costs. Efficient numerical approaches are therefore key to keep simulation cycles sufficiently short and tractable. In this talk an overview is given on recent methodological developments in terms of model building and numerical methods for coupled electro-mechano-fluidic models of the heart. Modeling applications will also be presented focusing on i) formation and maintenance mechanisms of cardiac arrhythmias; ii) treatment of arrhythmias by electrical defibrillation therapy and therapeutic optimizations based on optimal control theory; and iii) models for elucidating electro-mechanical disease mechanisms such as heart failure.