The mechanical function of the heart involves the fluid mechanics of the blood coupled to the passive elasticity of the flexible heart valve leaflets and the active elasticity of the muscular heart walls. We shall discuss a unified mathematical formulation of this problem of fluid-structure interaction, and also a numerical scheme for the computer solution of the coupled equations of motion. A prominent role in these equations is played by the fiber architecture of the cardiac tissue, and a mathematical theory whose purpose is to explain that fiber architecture will also be discussed. Computational results will be shown as a video animation of the heart, its valves, and the nearby great vessels, as well as the blood flow in the cardiac chambers. Still figures that capture the cardiac flow pattern in greater detail will also be shown.