The boundary of hyperbolic $n$-space, $\mathbb{H}^n$, has played an important role in the study of hyperbolic manifolds, the dynamics of hyperbolic isometries, and rigidity theorems. Many of these techniques extend to more general Gromov hyperbolic spaces and hyperbolic groups. In this talk we will discuss ways to construct analogous boundaries for non-hyperbolic spaces. Then we will address the question of to what extent these boundaries determine the underlying spaces and the groups that act on them.