Control of autonomous vehicles for applications such as surveillance, search, and exploration has been a topic of great interest over the past two decades. In particular, there has been a rising interest in control of multiple vehicles for reasons such as increase in system reliability, robustness, and efficiency, with a possible reduction in cost. The exploration problem is NP hard even for a single vehicle/agent, and the use of multiple vehicles brings forth a whole new suite of problems associated with communication and cooperation between vehicles. The persistent surveillance problem differs from exploration since it involves continuous/repeated coverage of the target space, minimizing time between re-visits. The use of aerial vehicles demands consideration of vehicle dynamic and endurance constraints as well. Another aspect of the problem that has been investigated to a lesser extent is the design of the vehicles for particular missions. The intent of this paper is to thoroughly review the persistent surveillance problem, with particular focus on multiple Unmanned Air Vehicles (UAVs), and present some of our own work in this area. We investigate the different aspects of the problem and slightly digress into techniques that have been applied to exploration and coverage, but a comprehensive survey of all the work in multiple vehicle control for search, exploration, and coverage is beyond the scope of this paper.