This chapter deals with oscillations of neurons and networks that are relevant for different cognitive processes, in particular for memory retention in animals and humans during sleep. This first section gives a brief insight into sleep and memory in nonmammalian species.The greatest amount of research on neuronal oscillations and plasticity has been conducted in vertebrates, more specifically on mammals. Studies on simpler invertebrate models-most notably the fruit fly and honey bee-have the advantage that the process of memory formation can more easily be dissected, from systems down to the molecular level, than for higher-order animals [1,2]. Despite well-established proof of memory and plasticity in these species, behavioral rather than electrophysiological definitions of sleep are up to now mostly employed [3,4]. Only very recently were 7-10 Hz oscillations discovered in the spontaneously sleeping fly [5]. In the olfactory nervous system of the Drosophila, several memory traces associated with short-term, intermediate, and long-term memory after conditioning with odors have meanwhile been reported [6]. For odor as well as for visual memories, a dynamic interaction between different brain regions across time reminiscent of memory in higher-order animals occurs [7,8]. Neuronal oscillations in the honey bee brain have not been published. Yet, not only was sleep found relevant for consolidating navigation memory [9], but presentation of a contextual odor during sleep enhanced subsequent retention performance [10]. Although the dependence on neuronal activity during sleep has, to the authors' knowledge, not yet been investigated, separate studies have revealed in crayfish both brain electric activity characteristic of sleep [11], as well as evidence of spatial and motor learning [12,13].