The Daya Bay experiment consists of functionally identical antineutrino detectors immersed in pools of ultrapure water in three well-separated underground experimental halls near two nuclear reactor complexes. These pools serve both as shields against natural, low-energy radiation, and as water Cherenkov detectors that efficiently detect cosmic muons using arrays of photomultiplier tubes. Each pool is covered by a plane of resistive plate chambers as an additional means of detecting muons. Design, construction, operation, and performance of these muon detectors are described.