Quantum field theory is a remarkably powerful tool: it describes a zoo of phenomena in systems ranging from tabletop condensed matter experiments to our largest particle colliders. In spite of these incredible successes, understanding the behavior of many interesting QFTs remains beyond our grasp. Various modern tools including dualities, which often exchange a mysterious strongly coupled description of a system with a more weakly coupled description of the same physics, typically help. In addition, at very long and very short distances, the symmetries of a QFT are often enhanced. In these regimes, interesting numerical measures arise that seem to obey simple rules when we compare these quantities at high energies and at low energies. Moreover, simplifying hidden algebraic structures can emerge as well. I will describe some of these numerical measures and hidden algebraic structures, the rules they obey, what they can tell us about QFT, and, if we are lucky, what they might have to say about the real world.