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Bose-Einstein condensation was first achieved in ultracold atomic gases almost twenty years ago. Since then, the manipulation and measurement of the resulting quantum-coherent fluids, and their fermionic analogues, has become a major field of scientific research. In this talk, I shall give an overview of the all-optical methods used to trap and cool such atomic gases. I shall then go on to describe some of the interesting phenomena so far observed, and also to say something about those (like Neel antiferromagnetism and perhaps even unconventional superconductivity) that remain elusive. The talk is non-technical, with an emphasis on the key concepts, and I assume as little prior knowledge of lasers or atomic physics as possible. All welcome!