It is reasonable to ask “What does a typical group look like?” or “Is it likely that a group satisfies property P?” To answer these questions requires some way of thinking probabilistically about groups. One way to do this -- the Gromov density model -- gives us a way to choose a group presentation at random. In this talk we’ll introduce this model of random groups and explore some of its properties. In particular, we will see why “most groups are hyperbolic” and we will touch on cubulation and Property (T).