There exist deep and yet still mysterious connections between nonlinear duality invariance and partially broken supersymmetry. This talk will review the general structure of U(1) duality-invariant models for nonlinear electrodynamics, including the famous ModMax theory. Generalisations of such models to supersymmetric and higher-spin cases will be briefly discussed. It will be shown that every flow in the space of U(1) duality-invariant nonlinear electrodynamics is generated by a function of the energy-momentum tensor. We will also explain that analogous TTbar-like results hold for self-interacting chiral 2-forms in six spacetime dimensions.
