Numerical simulation of the heart have the potential of improving the clinical practice for cardiovascular pathologies, which currently account for a large amount of deaths in the European adult population. The heart function arises from the interaction of several physical processes (including cardiac electrophysiology, muscular contraction and passive mechanical response, cardiac valves and blood dynamics). Moreover, these are characterized by widely varying characteristic times and lengths. Therefore, the numerical simulation of this complex system must rely on suitable techniques to deal with the multiphysics and multiscale nature of the problem. Finally, the large scale of the resulting systems requires the efficient use of HPC techniques. In this talk, we will discuss numerical methods to effectively couple the different subsystems in an efficient yet accurate and robust way. These will include staggered time discretization schemes to couple cardiac electrophysiology, mechanics and fluid dynamics, as well as suitable intergrid transfer operators that allow to solve each subsystem on a dedicated computational mesh, addressing computational efficiency, parallel scalability and robustness. The proposed methods are exploited to obtain realistic heart simulations, with biomarkers that closely match those of a healthy human heart.