Not only is the Apollonian configuration of circles an aesthetically noteworthy fractal but it also possesses a surprisingly rich mathematical structure. In particular, it conceals the main ingredients of modern physics, like Minkowski space-time, a model of spin, analogies of the quantum Aharonov-Bohm-like phenomena, and more. We shall gently explore these results, uncovering facts that should be found interesting and inspiring to students, researchers, and enthusiasts of geometry and physics.