When you look out on the universe at night, it does not seem like a very symmetrical place. Everywhere you look, you find vast empty space punctuated by galaxies of great energy and activity. Certainly this chaotic universe seems very different from symmetric objects of our usual experience like crystals or perfect Euclidean circles. Yet the universe is full of hidden symmetry! In this talk I will discuss these subtle symmetries, how they manifest themselves in our everyday experience, and how an even more subtle type of symmetry unlocks the subatomic world.