We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric configurations, given the graph automorphisms of their underlying set-configurations. Finally, we show how a specific class of combinatorial configurations called generalized cyclic configurations can be explored using this terminology, and give several interesting geometric results.