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The theoretical development of automatic control strategies for arterial blood pressure regulation is reviewed. The literature is classified by control strategy. Proportional-integral-derivative (PID) 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 using advanced control systems in this application. Issues regarding the use of control systems in the clinical environment are also discussed.