The representation theory of quantum groups has become an important area of research. For an integrable highest weight module of quantum groups, there exists a remarkable basis at q = 0, known as the crystal base, which was introduced by Kashiwara. It has a nice structure with respect to tensor products, and can be viewed as a colored oriented graph, called a crystal.

In this talk, we will briefly review crystal base theory, focusing on the case of gl_n. We will also explain how the crystal of an irreducible highest weight module can be identified with the set of semistandard Young tableaux.