The field of complex dynamics went through a rapid growth in the last several decades. Although the main conjecture (density of hyperbolicity) is yet to be solved, the dynamics of polynomial maps is nearly completely understood. On the other hand, the dynamics of non-polynomial rational maps still a wide open area of research. In my talk, I will discuss the notion of mating, which was first introduced by A. Douady and J. Hubbard. Mating is a way of factoring the dynamics of rational maps into separate components, each of which can be understood in terms of polynomial dynamics. After a brief introduction to the dynamics of quadratic polynomials, I will define mating, and state the main conjectures and results in this area. Then, I will present the content of my Master's thesis, which focuses on developing a new approach to the mating of polynomials.