A survey of the literature in which Liapunov's second method is used in determining the control Jaw is presented, with emphasis placed on the model-tracking adaptive control problem. Forty references are listed. Following a brief tutorial exposition of the adaptive control problem, the techniques for treating reduction of order, disturbance and time-varying parameters, multivariate systems, identification, and adaptive observers are discussed. The method is critically evaluated, particularly with respect to possibilities for application.