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.