Coverage is widely known in the field of sensor networks as the task of deploying sensors to completely cover an environment with the union of the sensor footprints. Related to coverage is the task of exploration that includes guiding mobile robots, equipped with sensors, to map an unknown environment (mapping) or clear a known environment (searching and pursuit- evasion problem) with their sensors. This is an essential task for robot swarms in many robotic applications including environmental monitoring, sensor deployment, mine clearing, search-and-rescue, and intrusion detection. Utilizing a large team of robots not only improves the completion time of such tasks, but also improve the scalability of the applications while increasing the robustness to systems’ failure. Despite extensive research on coverage, mapping, and exploration problems, many challenges remain to be solved, especially in swarms where robots have limited computational and sensing capabilities. The majority of approaches used to solve the coverage problem rely on metric information, such as the pose of the robots and the position of obstacles. These geometric approaches are not suitable for large scale swarms due to high computational complexity and sensitivity to noise. This dissertation focuses on algorithms that, using tools from algebraic topology and bearing-based control, solve the coverage related problem with a swarm of resource-constrained robots. First, this dissertation presents an algorithm for deploying mobile robots to attain a hole-less sensor coverage of an unknown environment, where each robot is only capable of measuring the bearing angles to the other robots within its sensing region and the obstacles that it touches. Next, using the same sensing model, a topological map of an environment can be obtained using graph-based search techniques even when there is an insufficient number of robots to attain full coverage of the environment. We then introduce the landmark complex representation and present an exploration algorithm that not only is complete when the landmarks are sufficiently dense but also scales well with any swarm size. Finally, we derive a multi-pursuers and multi-evaders planning algorithm, which detects all possible evaders and clears complex environments.