  The maximum mass of a neutron star has important implications across multiple
research fields, including astrophysics, nuclear physics and gravitational wave
astronomy. Compact binary millisecond pulsars (with orbital periods shorter
than about a day) are a rapidly-growing pulsar population, and provide a good
opportunity to search for the most massive neutron stars. Applying a new method
to measure the velocity of both sides of the companion star, we previously
found that the compact binary millisecond pulsar PSR J2215+5135 hosts one of
the most massive neutron stars known to date, with a mass of 2.27$\pm$0.16
M$_\odot$ (Linares, Shahbaz & Casares, 2018). We reexamine the properties of
the 0.33 M$_\odot$ companion star, heated by the pulsar, and argue that
irradiation in this "redback" binary is extreme yet stable, symmetric and not
necessarily produced by an extended source. We also review the neutron star
mass distribution in light of this and more recent discoveries. We compile a
list of all (nine) systems with published evidence for super-massive neutron
stars, with masses above 2 M$_\odot$. We find that four of them are compact
binary millisecond pulsars (one black widow, two redbacks and one redback
candidate). This shows that compact binary millisecond pulsars are key to
constraining the maximum mass of a neutron star.
