Sleep presents a paradox. It seems both perfectly natural and utterly mysterious. We love sleep and often can’t get enough of it, yet most of us have no idea what it is. But the paradoxes don’t stop there. All living creatures evolved to survive and avoid danger. Yet, animals of all kinds seem to simply shut down for several hours at a time, leaving themselves vulnerable to predation. What could be so important about sleep that animals evolved such a vulnerability? Not only that, but while we’re asleep we inhabit impossible worlds. They’re logically inconsistent, yet also perfectly understandable. While we’re dreaming, we rarely know that we’re dreaming. Yet, once we wake up, it’s immediately obvious that what we were experiencing just moments ago was completely absurd and couldn’t possibly be real. Nevertheless, during dreams it’s not uncommon to solve complex problems that would seem to require our (otherwise absent) powers of rationality. Other times, however, we seem not to dream at all or at least to not remember our dreams. How is it that our brains seem to effortlessly switch between these strange states of cognition back to normal waking cognition? What is sleep? What is its evolutionary function? What are dreams? Why do we only sometimes remember them?