Cluster algebras, introduced by Fomin and Zelevinsky, have been extensively studied over the past decade in a variety of different contexts. Although the definitions sound complicated, the underlying idea is fairly simple. From an initial seed (an n-tuple of formal variables) one obtains new seeds through a series of mutations, which amount to certain rational transformations. The axioms of cluster algebras imply some amazing properties. Among these is the Laurent phenomenon, which says that every rational function that results from a sequence of mutations is in fact a Laurent polynomial. I will attempt to define cluster algebras and provide enough examples to motivate the definition.