This paper reviews the theoretical development of automatic control strategies for arterial blood pressure regulation. The literature is classified by control strategy. Proportional-integral-derivative controllers, optimal controllers, adaptive controllers, and rule-based controllers are the most commonly encountered strategies in the literature. A brief description of each control scheme is given, followed by examples of each from the literature. Validation methods for the control performance vary from computer simulations to clinical tests on human patients. A number of reports of clinical success support the feasibility of advanced control systems in this problem. Issues on control systems in the clinical environment are also discussed.