  The Positron Puzzle is a half-century old conundrum about the origin of the
Galactic $\gamma$-ray emission line at photon energies of 511 keV, and the
shape of its morphology, showing a bulge-to-disk luminosity ratio of $\sim 1$ -
unlike any astrophysical source distribution. Positrons that have been cooled
to the eV scale capture electrons and form the intermediate bound state of
Positronium (Ps) which decays on a nano-second timescale into two or three
photons. Assuming the emission to originate from the Galactic bulge, centre,
and disk, a visible annihilation rate in the Milky Way of $\sim 5 \times
10^{43}\,\mathrm{e^+\,s^{-1}}$ has to be explained, either by a quasi-steady
state of production and annihilation, or by possibly multiple burst-like events
that flood the Galaxy with positrons, then fading away on a Myr timescale. In
this paper, I will review what the real Positron Puzzle is, where data and
simulations have been used inadequately which resulted in false claims and an
apparent quandary, what we really know and absolutely not know about the topic,
and how this epistemic problem might be advancing.
