A $\langle v, k, \lambda \rangle$-difference set is a nonempty proper subset $D$ of a finite group $G$ such that $|G| = v$, $|D| = k$, and each nonidentity element of $G$ can be written as $d_id_j^{-1}$ for $d_i, d_j \in D$ in exactly $\lambda$ different ways. Hadamard difference sets have the parameters $\langle 4m^2, 2m^2-m, m^2-m \rangle$ and provide a rich source of examples. While difference sets originally appeared in the study of symmetric designs and finite geometries, they now have applications and connections to these areas as well as to codes, groups, representations, and algebraic number theory. In this talk we will give some basic examples, see some results on the fundamental question of when difference sets exist for a given group or set of parameters, and approach the computationally difficult question of finding all difference sets in a given group.