  In this review we highlight a few physical properties of neutron stars and
their theoretical treatment inasmuch as they can be useful for nuclear and
particle physicists concerned with matter at finite density (and newly,
temperature). Conversely, we lay out some of the hadron physics necessary to
test General Relativity with binary mergers including at least one neutron
star, in view of the event GW170817: neutron stars and their mergers reach the
highest matter densities known, offering access to the matter side of
Einstein's equations. In addition to minimum introductory material for those
interested in starting research in the field of neutron stars, we dedicate
quite some effort to a discussion of the Equation of State of hadron matter in
view of gravitational wave developments; we address phase transitions and how
the new data may help; we show why transport is expected to be dominated by
turbulence instead of diffusion through most if not all of the star, in view of
the transport coefficients that have been calculated from microscopic hadron
physics; and we relate many of the interesting physics topics in neutron stars
to the radius and tidal deformability.
