The analysis of the efficiency and optimum use of cardiovascular and respiratory support systems is of great importance in research and development as well as in clinical practice. To understand the complex interaction between human cardiovascular or respiratory systems and the mechanical assist devices, a number of physical, computational or hybrid (physical-electrical or physical-computational) models/simulators have been developed and used in recent years. The hybrid models combine the advantages of both the physical models (interaction with assist devices) and of the computational/electrical models (accuracy, flexibility). This paper reviews the existing solutions and briefly describes their characteristics, advantages and disadvantages, chiefly emphasizing the features of the hybrid models that are most promising for future development.