recently well-measured neutron star masses, particularly near and above 2 solar masses, for the equation of state (EOS) of neutron star matter will be highlighted. Model independent upper
limits to thermodynamic properties in neutron stars, which only depend on the neutron star maximum mass, established from causality considerations will be presented. The need for non-perturbative treatments of quark matter in neutron stars is revealed through studies of self-bound quark matter stars, and of nucleon-quark hybrid stars. The extent to which several well-measured masses and radii of individual neutron stars can establish a model-independent EOS through an inversion of the stellar structure equations will be briefly discussed.