  Neutron star observations, including direct mass and radius measurements as
well as the analysis of gravitational wave signals emitted by stellar mergers,
provide valuable and unique insights into the properties of strongly
interacting matter at high densities. In this proceedings contribution, I
review recent efforts to systematically constrain the equation of state (EoS)
of dense nuclear and quark matter using a combination of ab initio particle and
nuclear physics calculations and astrophysical data. In particular, I discuss
the constraints that the gravitational wave observation GW170817 has placed on
the EoS, and comment on the future prospects of improving the accuracy, to
which this quantity is known.
