Promoting couplings to (background) fields is a useful and powerful technique to study all-order or nonperturbative properties of supersymmetric field theories. The case of the gauge coupling in N=1 supersymmetric gauge theories requires a non-standard treatment using a linear superfield. The corresponding current structure and anomaly matching or cancellation in effective lagrangian formulations lead then to a simple algebraic understanding of the all-order running of the gauge coupling (J / NSVZ beta function), while chiral currents respect the Adler-Bardeen theorem. 

(This talk is based on papers 1607.08646, 1609.00164 and earlier literature).