The list coloring problem is a variant of vertex coloring where a vertex may be colored only a color from a prescribed set. Several applications of vertex coloring are more appropriately modelled as instances of list coloring and thus we argue that it is an important problem to consider. Regardless of the importance of list coloring, few published algorithms exist for it. In this paper we review the only two existing ones we could find and propose an exact branch and bound one. We conduct an experimental evaluation of the three algorithms.