Our purpose is to discuss the idea of synchronization between two maps and applications of this idea. We are going to begin by giving a foundation in the theory of maps and how we plan to attack the problem. Once we have a basis established, we are going to move on and explore the idea of synchronization and how we can create it through coupling. We will look at the analysis of a specific problem, namely a system of two coupled quadratic maps. Finally we will look at how these results can be applied to more practical problems.