Supersymmetric field theories face the universal problem that the space of physical fields carries no representation of the supersymmetry algebra. Rather, the action is well-defined only after equations of motion are satisfied. I will review standard approaches that allow one to construct off-shell representations; the most general technique is the Batalin-Vilkovisky formalism, developed to deal with supergravity theories in which the action of this algebra is gauged. However, the BV approach has advantages even for less baroque theories; I will try and give an intuitive sense of what these advantages are, pointing out relations to Koszul duality, homotopy transfer of algebraic structures, and Noether's second theorem. This seminar gives an introduction to this week's "QGM seminar". The seminar is meant for Master and PhD students - all are welcome.