We summarize here the progress in identifying the neuronal network as well as the function of paradoxical sleep and the gaps of knowledge that should be filled in priority. The core system generating paradoxical sleep localized in the brainstem is now well identified, and the next step is to clarify the role of the forebrain in particular that of the hypothalamus including the melanin-concentrating hormone neurons and of the basolateral amygdala. We discuss these two options, and also the discovery that cortical activation during paradoxical sleep is restricted to a few limbic cortices activated by the lateral supramammillary nucleus and the claustrum. Such activation nicely supports the findings recently obtained showing that neuronal reactivation occurs during paradoxical sleep in these structures, and induces both memory consolidation of important memory and forgetting of less relevant ones. The question that still remains to be answered is whether paradoxical sleep is playing more crucial roles in processing emotional and procedural than other types of memories. One attractive hypothesis is that paradoxical sleep is responsible for erasing negative emotional memories, and that this function is not properly functioning in depressed patients. On the other hand, the presence of a muscle atonia during paradoxical sleep is in favour of a role in procedural memory as new types of motor behaviours can be tried without harm during the state. In a way, it also fits with the proposed role of paradoxical sleep in setting up the sensorimotor system during development.