One way to study a class of geometric objects is to try to find and study its moduli space— another geometric space whose points represent isomorphism classes of objects. One can then study geometric properties of the objects in question by studying the geometry of this moduli space. Unfortunately, it is often impossible to find such a moduli space. In this talk, I hope to motivate what one would like to have in a moduli space, and why we might have trouble finding one. The goal will be to look at what happens when we try to look for a moduli space of triangles, which already exhibits many of the interesting phenomena common to the study of moduli spaces and stacks.