Recent conceptual advances have allowed us to delve farther than ever before into the quantum corrections of scattering amplitudes, perhaps nature's most perfect microscopic structures. Doing so we have uncovered surprisingly simple relations universal to gauge and gravity theories. These are revolutionizing our way of calculating quantities in quantum field theory, and promise to definitively answer outstanding open questions such as the existence of four-dimensional finite quantum field theories of gravity, as well as leading to new questions regarding dual descriptions of the theories themselves. I will spend the majority of my talk discussing these and other related advances with an emphasis on the driving ideas and concrete results. Fascinatingly, stochastically-sourced classical field theories allow us to apply many of our familiar tools to open problems in precision cosmology. I will conclude with an introduction to the exciting first stages of just such a program: establishing an effective field theory of large scale structure in the early universe.