This paper reviews the main aspects of cardiovascular system dynamics with emphasis on modeling hemodynamic characteristics using a lumped parameter approach. Methodological and physiological aspects of the circulation dynamics are summarized with the help of existing mathematical models: The main characteristics of the hemodynamic elements, such as the heart and arterial and venous systems, are first described. Lumped models of micro-circulation and pulmonary circulation are introduced. We also discuss the feedback control of cardiovascular system. The control pathways that participate in feedback mechanisms (baroreceptors and cardiopulmonary receptors) are described to explain the interaction between hemodynamics and autonomic nerve control in the circulation. Based on a set-point model, the computational aspects of reflex control are explained. In final chapter we present the present research trend in this field and discuss the future studies of cardiovascular system modeling.