The anatomy and motion of the heart and the aorta are essential for patient-specific simulations of cardiac electrophysiology, wall mechanics and hemodynamics. Within the European integrated project euHeart, algorithms have been developed that allow to efficiently generate patient-specific anatomical models from medical images from multiple imaging modalities. These models, for instance, account for myocardial deformation, cardiac wall motion, and patient-specific tissue information like myocardial scar location. Furthermore, integration of algorithms for anatomy extraction and physiological simulations has been brought forward. Physiological simulations are linked closer to anatomical models by encoding tissue properties, like the muscle fibers, into segmentation meshes. Biophysical constraints are also utilized in combination with image analysis to assess tissue properties. Both examples show directions of how physiological simulations could provide new challenges and stimuli for image analysis research in the future.