This contribution addresses the mathematical modeling and numerical approximation of the excitation-contraction coupling mechanisms in the heart. The main physiological issues are preliminarily sketched along with an extended overview to the relevant literature. Then we focus on the existing models for the electromechanical interaction, paying special attention to the active strain formulation that provides the link between mechanical response and electrophysiology. We further provide some critical insight on the expected mathematical properties of the model, the ability to provide physiological results, the accuracy and computational cost of the numerical simulations. The paper ends with a numerical experiment studying the electromechanical coupling on the anisotropic myocardial tissue.