The way that we understand, teach, and use quantum field theory to make predictions for experiments is rapidly changing in order to make the simplicity of our predictions less surprising (and hence also easier to compute). Indeed, whether for theoretical exploration or practical applications, the methods described in textbooks are no longer those being used by experts today.

In this talk, I will describe some of our recent advances that have been made to explain this simplicity and how they have been used to dramatically extend predictive reach. Much of this progress has so far been made for especially simple quantum field theories, but many of the lessons learned have much wider applicability. I will describe the status of these generalizations today, and the concrete roads ahead.