The bulge of our Galaxy is illuminated by the 0.511 MeV gamma-ray line flux from annihilations of nonrelativistic positrons. The emission is strongly concentrated at the Galactic Center, in contrast to gamma-ray maps tracing nucleosynthesis (e.g., the 1.809 MeV line from decaying ^26Al) or cosmic ray processes (e.g., the 1-30 MeV continuum), which reveal a bright disk with a much less prominent central region. Central to resolving the origin of the positrons is the question of their injection energies, which range up to 100 MeV or even higher in recent astrophysical and exotic (requiring new particle physics) models. If positrons are generated at relativistic energies, higher-energy gamma rays will also be produced from inflight annihilation of positrons on ambient electrons. I will discuss recent observations of the 0.511 MeV gamma-ray line, constraints imposed on the injection energies of Galactic positrons from inflight annihilations and implications on astrophysical and e xotic models proposed to explain the origin of positrons.