What are quasicrystals, and what's "quasi" about them? In fact there is nothing quasi about them - quasicrystals are real crystals. But then what is a crystal? Recent research in aperiodic order, tiling theory, and diffraction theory on the one hand, and in the experimental sciences on the other, suggests surprising answers to this question. In this talk, for non-specialists, I will describe some of the answers, and some still-open questions.