In this talk, we will define what an Apollonian Circle Packing is, and the properties associated to these packings, including the Apollonian group, the relationship with binary quadratic forms, and obstructions that appear within the curvatures. The Local-to-Global conjecture for Apollonian circle packings was recently disproven, and we will discuss the development of this conjecture, how it was disproven using quadratic reciprocity, and the new conjecture.