This dissertation presents novel motion coordination, planning, and control algorithms to solve visibility problems for mobile sensor networks and UAVs (Unmanned Air Vehicles). These are problems where an autonomous system must move in such a way that it achieves or maintains line of sight of some object(s) of interest in a nonconvex environment. More specifically, we address variations of the following three problems: (1) How should a group of camera-equipped robotic agents deploy into an environment in order to achieve full visibility of that environment, (2) how can the rotations of security cameras be coordinated to ensure an intruder is caught on video, and (3) what path should a UAV follow in order to photograph a set of suspicious vehicles in a city as quickly as possible? We find answers to these questions using a unique blend of tools from the research domains of computational geometry, combinatorics, robot motion planning, and control theory.