This talk is based on joint work with Kyle Austin. In the study of C*-algebras, focusing on those arising via a groupoid construction can provide access to additional structural information while still allowing for a wealth of examples. My goal in this talk is to describe a method of approximating the groupoid structure, enabling us for example to extend results from second countable groupoids to sigma-compact groupoids. To that end, I will discuss inverse systems of groupoids and their dual directed systems of groupoid C*-algebras. I will conclude with some applications of this work to C*-algebra theory.