We'll review the definition of the elliptic genus and some of its history. In particular, we'll see that it is related to classical invariants such as the signature and the $\hat A$-genus, and how the rigidity of the elliptic genus generalizes classical theorems on spin manifolds. In this context, we'll notice that $\pi_2$-finite manifolds behave a little like spin manifolds under $S^1$ actions, and discuss the topological consequences of this similarity and applications.