By establishing the probabilities of scattering events, quantum field theories realize predictions for our most ambitious and reaching high-energy experiments. Yet the sector of the Standard Model describing the strong force has largely been resistant to calculation using Feynman diagrams for all but the most simple processes, even with our biggest arrays of computers running months to years at a time. Textbook approaches simply collapse under the weight of a redundancy dragged throughout. These complications in quantum gauge theories presage a far greater explosion of terms in applying standard methods to quantum gravity calculations -- calculations at the heart of some of our most fundamental questions. Yet, when carried out, the end results are incredibly compact. After all, scattering within gauge and gravity theories should represent nature's most perfect microscopic encoding of state evolution -- governed as they are by simple ideas of symmetry. Indeed, recent exploration organized around manifestly physical information has uncovered not only remarkable simplicity, but surprisingly good high-energy behavior of gravitational interaction. I will discuss many of these developments, emphasizing concrete results, driving ideas, and future directions.