Probing new physics with Galactic (keV-MeV) gamma-ray emission

Measurements of the 511 keV emission reveal the presence of a steady injection of positrons that is very concentrated around the Galactic bulge, and whose origin remains unknown. I will review the current state of the "positron puzzle" and show how we can use the observations of the 511 keV line to constrain the properties of beyond Standard Model particles, such as sub-GeV dark matter, or feebly interacting particles (e.g. sterile neutrinos or axion-like particles), as well as satellite-mass primordial black holes. In addition, I'll show that other mechanisms of (keV to MeV) continuum photon emission associated to the production of positrons can improve existent constraints.