The relationship between subshifts of finite type over a finite alphabet and edge shifts for a finite, essential directed graph is well-known. Over the last 10 years it has been shown that it is possible to associate a C*-algebra, called a graph algebra to an arbitrary directed graph. It turns out that there is a quite a strong relationship between properties of the directed graph and the graph algebra, moreover these properties have important dynamical ramifications. The purpose of this talk is to try to give a non-technical exposition of the relationship between a graph algebra and the associated subshift of finite type.