Mathematical models have been used in physiological research for centuries, but they have so far played a less important role than in many other branches of science. Important reasons for this include the extreme complexity and multi-scale nature of biological systems, which makes it challenging both to derive accurate models and to solve the resulting mathematical equations. With the increasing availabilty of powerful computer hardware and numerical software, accompanied by a revolutionary increase of knowledge in molecular biology, this situation is currently about to change. The last ten years in particular, we have seen the advent of increasingly accurate mathematical models of physiological systems, linking biophysical processes across a wide range of spatial and temporal scales. An illustrative example is mathematical models of heart electrophysiology and mechanics, where models have been derived that link processes on cellular and sub-cellular level to the function of the complete organ. Although modeling of other components of the body lags behind that of the cardiovascular system, there is an ongoing development to model other organs and organ systems. Profiled initiatives in this direction include the IUPS Physiome project (http://www.physiome.org.nz) and the Virtual Physiological Human (http://www.europhysiome.org). Although slightly differing in focus, the vision of both these initiatives is to construct advanced computational models of the complete human body, which may be used both for clinical work and as test beds for new physiological hypotheses. In this talk we present a few examples of mathematical models describing physiological phenomena, and how they have been used to verify and quantify physiological and clinical knowledge. The focus will be on mathematical models of the cardiovascular system.