Enlarge (credit: Imagen Rafael Cosme Daza ) Most creatures sleep, but until now, REM (rapid eye movement) sleep, the phase of sleep in which dreams occur, was thought to be exclusive to vertebrates. Octopuses appear to be the first invertebrates to show they are also capable of this When it comes to neural function, studies have found these cephalopods are more like us than we think (pun somewhat intended).