Abstract: “I will review some recent progress in analyzing strongly coupled quantum field theories, focusing on theories with supersymmetry. In addition to their role in particle physics, supersymmetric theories are an ideal theoretical laboratory for deepening our understanding of quantum field theory and the diverse phenomena it describes. I will showcase a selection of new tools that have been developed for such theories — notably the algebraic properties of conserved currents and their coupling to background fields. This leads to general constraints on renormalization group flows in diverse dimensions, restrictions on the properties of bound states and solitons, and the construction of new exactly computable observables defined by placing the field theory on a curved manifold.”