  Recent advances in neutron star observations have the potential to constrain
the properties of strongly interacting matter at extreme densities and
temperatures that are otherwise difficult to access through direct experimental
investigation. At the same time, chiral effective field theory has developed
into a powerful theoretical framework to study nuclear interactions and nuclear
matter properties with quantified uncertainties in the regime of astrophysical
interest for modeling neutron stars. In this article, we review recent
developments in the chiral effective field theory approach to constructing
microscopic nuclear forces and focus on many-body perturbation theory as a
computationally efficient tool for calculating the structure, phases, and
linear-response properties of hot and dense nuclear matter. We also demonstrate
how effective field theory combined with Bayesian methods enables statistically
meaningful comparisons between nuclear theory predictions, nuclear experiments,
and observational constraints on the nuclear equation of state.
