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In this talk I will introduce some of the combinatorics behind affine permutations. These are a generalization of classical permutations that, when viewed as a reflection group, amount to adding an affine reflection to the set of generators (hence the name). We now end up with an infinite group, however, many of the same results from classical permutations still hold. Classifying families of permutations in terms of the patterns they avoid has been studied for a long time. However, applying pattern avoidance to affine permutations is fairly new. I will discuss pattern avoidance, and in particular, the role it plays in the geometry of the corresponding affine Schubert varieties. Part of this talk is joint work with Sara Billey.