Although sleep is a very conspicuous behavior in all animals that we are frequently in contact with and possibly in many others, its scientific study was for many years restricted to very few of them. However, since the end of the XX century there have been studies about sleep in several animals and currently many of them attempt to found, first, if all animals sleep and second, if their sleep is similar to that of other animals. An important objective of this search is to identify the animal species in which sleep originated, which might gives us clues about the need that was fulfilled by such behavior. The search started with insects, among the most developed arthropods, but has now been expanded to include other invertebrates, among them crustaceans. In this work we review some aspects of sleep in invertebrates, focusing on the crustacean crayfish, animals in which both, behavioral and electrophysiological studies have been conducted and whose results show surprising similarities with sleep in mammals.