A 1979 theorem of Belyi tells us that an algebraic curve is defined over Q-bar iff its corresponding Riemann surface admits a morphism to P^1 with at most three branching values. I'll discuss some aspects of the proof of this theorem, and sketch the beginnings of Grothendieck's theory of "dessins d'enfants" (children's drawings), which was inspired by Belyi's work. There will be examples!