It is fair to say, following Max Noether, that while the moduli space of stable algebraic curves was created by God, the moduli space of stable algebraic surfaces was designed by the Devil. While the former space has a beautiful well-understood geometry, the latter space is known, among other things, to possess literally arbitrary singularities! However, for some surfaces we have a good idea how the moduli space looks like. I will give a survey of these results and techniques used to prove them. The talk will be accessible to graduate students.