Integrable cross-ratio maps are solutions to one of the discrete integrable equations on quad-graphs. These maps may be of interest to many mathematicians; just to name a few uses, discrete holomorphic functions, orthogonal circle packings, and polygon recutting are all special cases of integrable cross-ratio maps. The goal of my research is to find an explicit (non-recursive) formula for a certain cross-ratio system. In this talk, we will examine the cross-ratio system and observe some of its properties, such as multidimensional consistency. We will then discuss some of my work creating and using combinatorial structures to find and characterize solutions in these systems.