This chapter gives an overview of various ventricular assist devices with a particular focus on axial flow pumps. Using the Hemopump as an example, we developed a model of a canine circulatory system assisted by an axial flow pump, and used computer simulation to predict the effects of the assist device under various hemodynamic conditions. In general, the results from the simulation are in good agreement with that observed in clinical and animal experiments. The same model is further used to explore the techniques and strategy for optimum control of the assist device by introducing an objective function, and choosing suitable membership functions with associated weighting factors, the model offers great flexibility in choosing the targeted hemodynamic variables, in specifying the particular way that each of these variables is to be optimized, and in assigning the relative importance of each targeted variable. The methods used and the results obtained in this study can be incorporated into the design of an advanced physiological controller for a long-term operation of the axial flow pump-based assist device as well as other types of continuous-flow LVAD.