Supervisory Decision-Making (SDM) refers to human supervision of several semi-autonomous (nonhuman) systems in a collaborative manner to accomplish a goal. This study defined SDM and distinguished it from traditional supervisory control and decision-making. An examination of diverse literature in organization design, biology, robotics, innovation diffusion, and trust in automation, yielded no directly applicable or comprehensive models. Field observations were made of large-scale war-games, where operators interacted with semi/autonomous sensors and defense-management systems. Four cognitive models were subsequently developed describing 1) adaptive partnering with automation, 2) technology adoption, 3) trust in automation, and 4) dealing with advice from decision aids. The latter quantitatively models individual, dynamic decisions to accept or reject recommendations made by automated battlespace advisors. The anticipated benefits of this work include more effective human-robot coordination, communication, the identification of experiments, and ultimately design guidelines for robotics, intelligent software agents, intelligent transportation systems, and space exploration.