This article presents a broad overview of the fluid mechanics of the human cardiovascular system. Beginning in the heart, we travel through the main features of our circulation to highlight important functions and diseases where fluid mechanics plays a central role. Of particular focus is the role of computational modelling in uncovering the dynamic flow phenomenon throughout our body, its association with cardiovascular disease mechanisms and progression and its importance in clinical treatment planning. We also emphasize the multiscale nature of the cardiovascular system, and associated challenges. The main aim of this review is to highlight progress and ongoing challenges in our understanding of cardiovascular haemodynamics, as well as the future outlook for translating the current state-of-the-art to widespread clinical application and improved patient outcomes.