Sleep is widespread across the animal kingdom. However, most comparative sleep data exist for terrestrial vertebrates, with much less known about sleep in amphibians, bony fishes, and invertebrates. There is an absence of knowledge on sleep in cartilaginous fishes. Sharks and rays are amongst the earliest vertebrates, and may hold clues to the evolutionary history of sleep and sleep states found in more derived animals, such as mammals and birds. Here, we review the literature concerning activity patterns, sleep behaviour, and electrophysiological evidence for sleep in cartilaginous (and bony) fishes following an exhaustive literature search that found more than 80 relevant studies in laboratory and field environments. Evidence for sleep in sharks and rays that respire without swimming is preliminary; evidence for sleep in continuously swimming fishes is currently absent. We discuss ways in which the latter group might sleep concurrent with sustained movement, and conclude with suggestions for future studies in order to provide more comprehensive data on when, how, and why sharks and rays sleep.