The human heart is a complex electromechanical pump, translating electrophysiological stimulation into tissue contraction and the ejection of blood from its chambers to drive cardiovascular blood flow. Despite being incredibly adaptable and robust, the human heart can experience a myriad of maladies leading to disruption and dysfunction. Core to cardiac physiology, and pathophysiology, is the efficient interaction between solid tissue and blood, translating mechanical work into blood flow. Understanding this interaction, principles of fluid mechanics, turbulence and fluid-structure interaction provide a core foundation. From recent work on image-based estimation of pressure loss, to analytic solutions and computational methods for fluid-structure interaction, to multigrid-in-time, this talk will explore some of the mathematical techniques useful for evaluating the behavior of blood and its impact on the heart.