Understanding the structure of factor maps for a category of dynamical systems is important for understanding the relationships between dynamical properties of objects within that category. In the case of finite alphabet symbolic dynamics, The Curis-Hedlund-Lyndon Theorem, a fundamental result in the study of symbolic dynamics, gives a complete description of these factor maps for the symbolic dynamics of a group G over some alphabet A. In this talk we will go through the argument of the theorem, make connections to the widely studied case where G is the group of the integers, and then, if time allows, present a counterexample to the theorem in the case of an infinite alphabet.