In the past decade, the technique of associating a C*-algebra to a directed graph has provided a useful tool for modeling many well-known classes of C*-algebras --- particularly, classes of C*-algebras related to dynamical systems. More recently, algebraists have been interested in associating algebras, known as Leavitt path algebras, to directed graphs. It turns out that each Leavitt path algebra sits as a dense *-subalgebra in a graph C*-algebra, and the structures of the two objects are intimately related. We will discuss interactions of the graph algebra theories with the Classification Program. In particular, we'll see that graph algebras can be used to model and provide insights for certain classifiable C*-algebras; and conversely, we'll show how classification results have applications to the graph algebra theories.