This talk will be a gentle introduction to conformal geometry in the Riemannian and pseudo-Riemannian settings. We'll start by defining the hyperboloid model of hyperbolic space, and considering the group of isometries acting on this model. These isometries preserve the boundary sphere of the hyperbolic ball, raising the question of whether there is a geometric structure on the boundary preserved by this action. Spoiler: it's the conformal structure! If we have time, we'll also tackle Einstein spaces, the model spaces for pseudo-Riemannian conformal geometry.