A circle packing is the mathematical name for a collection of circles. I am interested in circle packings with a fixed pattern of tangencies between the circles. Given a tangency pattern, one might ask questions like, “Can I find a circle packing with that tangency pattern?” and “How many such circle packings can I find?” and “What does the collection of all such circle packings look like?”. The classical Koebe-Andreev-Thurston Circle Packing Theorem gives an answer to these questions for some classes of circle packings. In my talk, I’ll give an introduction to circle packings and discuss the Koebe-Andreev-Thurston Theorem. I’ll also talk about ideas for expanding these questions to other types of packings.