Moduli spaces are spaces whose points parametrise geometric objects of some kind, and are an important tool in algebraic geometry and many other areas of mathematics and physics. In this talk, I will explain the formalism of moduli problems, or moduli functors, which is one way of getting a rigorous handle on the notion of moduli space. The focus of the talk will be on examples, such as Grassmannians, Hilbert schemes, and, time permitting, moduli spaces of curves. In each case, I will write down the moduli problem and sketch a more (or less) explicit construction of the moduli space.