Comprehension of the beating of the human heart is important for cardiac research and will improve many clinical applications. Simulations based on models describing cardiac electro-mechanics can acquire insights into this behavior. This work focuses on the mathematical reconstruction of electrophysiology, excitation conduction, and tension development in the human heart on the cellular and the tissue level. The tissue models represent accurate anatomical shapes of the atria and the ventricles and incorporate electrophysiological heterogeneity and anisotropic conduction. The simulations comprehend the physiological behavior of the ventricles and of the atrium including the sinoatrial node as well as pathological cases like ventricular and atrial fibrillation and genetic defects in ionic channels.