Despite the overwhelming wealth of data available today, gaining mechanistic insight into cardiac function remains to be a challenging endeavour due to the multiscale/multiphysics nature of cardiac function, where complex interactions of processes arise within and across levels of organization, as well as between electrical, mechanical and fluidic systems. Computer simulation has become a powerful adjunct to experimental studies, but current modeling methodology imposes severe limitations, forcing research to resort to overly simplified modeling assumptions. This talk will highlight recent methodological advances in terms of modeling organ scale cardiac anatomy and electro-mechano-fluidic function at high spatial resolution. The presented methods aim at lifting many of the current modeling restrictions to enable computational studies where model complexity is chosen as a function of the question being addressed, and not based on feasibility constraints. The use of advanced numerical methods is of pivotal importance to reduce execution times, thus facilitating quick simulation-analysis cycles. Application examples will be presented including multiscale arrhythmogenic effects due to mitochondrial dysfunction and calcium handling, as well as clinical modeling studies which aim at optimization and outcome prediction due to interventions such as aortic valve replacement and repair of aortic coarctations.