This paper surveys recent results in coverage path planning for mobile robots. Coverage path planning is a new approach that determines a path for a robot to pass over all points in its free space. Unlike conventional point-to-point path planning, coverage path planning is used in applications such as robotic demining, snow removal, lawn mowing, car-body painting, and machine milling. The paper focuses on coverage path planning algorithms for mobile robots constrained to operate in the plane, which can be classified as either heuristic or complete. It is conjectured that most complete algorithms use an exact cellular decomposition, either explicitly or implicitly, to achieve coverage. The paper organizes coverage algorithms into four categories: heuristic, approximate, partial-approximate, and exact cellular decompositions. The final section describes some provably complete multi-robot coverage algorithms. Motion planning algorithms originally considered the start-goal problem, which determines a path between two points. The motion planning literature includes many elegant solutions to this problem. Map-based approaches allow for more efficient path generation, as they require a one-time fixed cost to construct the map and a small cost each time to generate paths. However, conventional path planning algorithms do not address applications such as floor cleaning, lawn mowing, mine hunting, and painting, which require coverage path planning. Coverage path planning emphasizes the space swept out by the robot's sensor, and integrating the robot's footprint along the coverage path yields an area identical to that of the target region. This problem is related to the covering salesman problem, a variant of the traveling salesman problem. This paper overviews recent work in coverage path planning for mobile robots. Some early work in coverage path planning relies on heuristics, which are simple rules of thumb that may work well but do not have provable guarantees. Recent works have achieved provable guarantees by ensuring the planner generates a path that completely covers the free space. This is important for applications such as de-mining, where using a heuristic is akin to using a faulty mine detector. Many coverage path planners use a cellular decomposition of the free space to achieve coverage. A cellular decomposition breaks down the target region into cells such that coverage in each cell is "simple." Provably complete coverage is attained by ensuring the robot visits each cell in the decomposition. The paper also addresses issues such as time-to-completion, the availability of a priori information, and the use of randomized approaches.This paper surveys recent results in coverage path planning for mobile robots. Coverage path planning is a new approach that determines a path for a robot to pass over all points in its free space. Unlike conventional point-to-point path planning, coverage path planning is used in applications such as robotic demining, snow removal, lawn mowing, car-body painting, and machine milling. The paper focuses on coverage path planning algorithms for mobile robots constrained to operate in the plane, which can be classified as either heuristic or complete. It is conjectured that most complete algorithms use an exact cellular decomposition, either explicitly or implicitly, to achieve coverage. The paper organizes coverage algorithms into four categories: heuristic, approximate, partial-approximate, and exact cellular decompositions. The final section describes some provably complete multi-robot coverage algorithms. Motion planning algorithms originally considered the start-goal problem, which determines a path between two points. The motion planning literature includes many elegant solutions to this problem. Map-based approaches allow for more efficient path generation, as they require a one-time fixed cost to construct the map and a small cost each time to generate paths. However, conventional path planning algorithms do not address applications such as floor cleaning, lawn mowing, mine hunting, and painting, which require coverage path planning. Coverage path planning emphasizes the space swept out by the robot's sensor, and integrating the robot's footprint along the coverage path yields an area identical to that of the target region. This problem is related to the covering salesman problem, a variant of the traveling salesman problem. This paper overviews recent work in coverage path planning for mobile robots. Some early work in coverage path planning relies on heuristics, which are simple rules of thumb that may work well but do not have provable guarantees. Recent works have achieved provable guarantees by ensuring the planner generates a path that completely covers the free space. This is important for applications such as de-mining, where using a heuristic is akin to using a faulty mine detector. Many coverage path planners use a cellular decomposition of the free space to achieve coverage. A cellular decomposition breaks down the target region into cells such that coverage in each cell is "simple." Provably complete coverage is attained by ensuring the robot visits each cell in the decomposition. The paper also addresses issues such as time-to-completion, the availability of a priori information, and the use of randomized approaches.