Introduction P pointing control and rapid maneuvering capabilities have long been part of many space missions; examples include military observation platforms, communications satellites, and exploratory space missions. Rapid retargeting may be an intrinsic part of the mission profile, as in military and exploratory applications, or it may be required to correct, periodically, the guidance and navigation sensors of a spacecraft. Consequently, research in attitude maneuvers and time-optimal controls has been a consistently strong field of study. Of particular interest is the time-optimal attitude maneuver; this problem combines aspects of many different fields, such as mathematics, optimal control theory, spacecraft dynamics, elasticity, and structural mechanics. In the study of attitude maneuvers and control, researchers have investigated the response of satellite control systems to disturbances caused by the influence of solar pressure, gravity gradients, the effectiveness of active control devices, and the best placement of actuators and sensors on a given structure. Numerous studies have been conducted for specific satellite configurations to determine a time-optimal attitude control for a predetermined maneuver. Further, the mathematical procedures required to investigate this problem have inspired a number of papers on techniques to address the difficulties which arise from time-optimal control. This survey reviews the literature of the last thirty years, including many of the more recent advances in the field, covers the aforementioned topics as well as specific attitude maneuvers, and traces the development of time-optimal and near time-optimal control algorithms. We begin by considering the formulation of the time-optimal control problem and the difficulties faced in obtaining the solution. The equations for the rotational motion of any rigid body (Ruler's equations) are quite elegant and compact; they are also coupled and highly nonlinear. In addition, the high angular velocities of time-optimal maneuvers will cause gyroscopic stiffness through the nonlinear terms. Ruler's equations are expressed as