The edit distance problem relates to questions in theoretical computer science but there are also some origins in evolutionary biology. In computing edit distance, we want to know how many deletions or additions of edges in a graph are required in order to eliminate a specified induced subgraph. We will describe the problem in full, giving some of the basic results and techniques for finding bounds on edit distance. In the process, we will define the so-called binary chromatic number, and show how it bounds the edit distance. Furthermore, we will see how the problem relates to Szemeredi's regularity lemma, Turan's theorem and Ramsey theory.