The deployment of multiple robots for achieving a common goal helps to improve the performance, efficiency, and/or robustness in a variety of tasks. In particular, the observation of moving targets is an important multirobot application that still exhibits numerous open challenges, including the effective coordination of the robots. This paper reviews control techniques for cooperative mobile robots monitoring multiple targets. The simultaneous movement of robots and targets makes this problem particularly interesting, and our review systematically addresses this cooperative multirobot problem for the first time. We classify and critically discuss the control techniques: cooperative multirobot observation of multiple moving targets, cooperative search, acquisition, and track, cooperative tracking, and multirobot pursuit evasion. We also identify the five major elements that characterize this problem, namely, the coordination method, the environment, the target, the robot and its sensor(s). These elements are used to systematically analyze the control techniques. The majority of the studied work is based on simulation and laboratory studies, which may not accurately reflect real-world operational conditions. Importantly, while our systematic analysis is focused on multitarget observation, our proposed classification is useful also for related multirobot applications.