How can we arrange an infinite number of spheres to maximize the proportion of space they occupy? Kepler conjectured that the "cannonball" packing is the optimal way to do it. This conjecture remained unproved for almost 400 years until Hales and Ferguson provided a 250-page proof accompanied by hundreds of thousands of lines of computer code. Given an infinite number of coins of three fixed radii, how can we place them on the plane to maximize the proportion of the covered surface? A disc packing is called triangulated if its contact graph is triangulated. We identified optimal packings for several triplets of disc sizes, all of which are triangulated. Conversely, we also showed that for certain other triplets, no triangulated packing is optimal. Building on our expertise in multi-size disc packings, we extend our research to two-sphere packings. Simplicial sphere packings are those whose contact graphs form pure simplicial 3-complexes. We consider the only ratio of sphere sizes that allows such packings which are conjectured to be optimal.