We present recent developments in cardiac modeling that improve the understanding of the intricate interplay between electrophysiology, mechanical activation, and passive mechanical response within the human heart. We unveil a state-of-the-art approach that integrates advanced models for these core components, resulting in a coupled electromechanical problem that offers a comprehensive representation of physiological and pathological conditions. The model seamlessly couples a 3D electromechanical framework with a 0D closed-loop model of systemic and pulmonary blood circulations. To approximate the spatial aspects of the involved PDEs, we employ the Finite Element method. Numerical solutions to the coupled electromechanical problem are achieved through partitioned-staggered schemes, enhancing computational efficiency and stability. These simulations, executed within a high-performance computing framework, provide insights into cardiac electromechanics in diverse scenarios, shedding light on both normal and pathological cardiac behavior. Furthermore, our focus extends to multiphysics and multiscale models for simulating the hemodynamics of the human heart, with particular attention on fluid-structure interaction problems. Finally, we introduce a novel machine learning method that facilitates real-time numerical simulations, paving the way for the creation of a cardiac digital twins. This innovative approach not only streamlines the simulation process but also opens avenues for personalized and patient-specific modeling in the realm of cardiac electrophysiology and mechanics. This project has received funding from the research grant PRIN 2022 (MUR Italy) 202232A8AN “Computational modeling of the human heart: from efficient numerical solvers to cardiac digital twins”, 2023-2025.