Abstract: Classic subdifferentials in variational analysis may fail to fully represent the Bregman proximal operator in the absence of convexity. In this talk, we fill this gap by introducing the left and right Bregman level proximal subdifferentials and investigate them systematically. Every Bregman proximal operator turns out to be the resolvent of a Bregman level proximal subdifferential under a standard range assumption, even without convexity. Aided by this pleasant feature, we establish new correspondences among useful properties of the Bregman proximal operator, the underlying function, and the Bregman level proximal subdifferential, generalizing classical equivalences in the Euclidean case. Unlike the classical setting, asymmetry and duality gap emerge as natural consequences of the Bregman distance. Along the way, we improve results by Kan and Song and by Wang and Bauschke on Bregman proximal operators. We also characterize the existence and single-valuedness of the Bregman level proximal subdifferential, investigate coincidence results, and make an interesting connection to relative smoothness. Joint work with Andreas Themelis.