Measurements of the 511 keV emission reveal the presence of a steady injection of positrons that is very concentrated around the Galactic centre, and whose origin remains unknown. While astrophysical sources do not easily fit the observed morphology and intensity of this excess, MeV dark matter has been proposed as a compelling explanation with interesting consequences. In this seminar, I will introduce the "positron puzzle" and discuss its correlation to other anomalous emissions at the Galactic centre, especially focusing on the observational consequences of the dark matter explanation of the 511 keV excess. Finally, I’ll show how these observations can be used to constrain the properties of asteroid-mass primordial black holes and beyond Standard Model particles, such as sterile neutrinos or axion-like particles.