During the past two decades, chiral effective field theory has become a popular tool to derive nuclear forces from first principles. Two-nucleon interactions have been worked out up to sixth order of chiral perturbation theory and three-nucleon forces up to fifth order. Applications of some of these forces have been conducted in nuclear few- and many-body systems—with a certain degree of success. But in spite of these achievements, we are still faced with great challenges. Among them is the issue of a proper uncertainty quantification of predictions obtained when applying these forces in ab initio calculations of nuclear structure and reactions. A related problem is the order by order convergence of the chiral expansion. We start this review with a pedagogical introduction and then present the current status of the field of chiral nuclear forces. This is followed by a discussion of representative examples for the application of chiral two- and three-body forces in the nuclear many-body system including convergence issues.

We calculate total masses and radii of neutron stars for pure neutron matter and nuclear matter in β equilibrium. We apply a relativistic nuclear matter equation of state derived from Dirac-Brueckner-Hartree-Fock calculations. We use realistic nucleon-nucleon interactions defined in the framework of the meson exchange potential models. Our results are compared with other theoretical predictions and recent observational data. Suggestions for further study are discussed.

We present and discuss predictions for a cross section of bulk and single-particle properties in symmetric nuclear matter based on recent high-quality nucleon-nucleon potentials at ${\mathrm{N}}^3\mathrm{LO}$ and including all subleading three-nucleon forces. We begin with the equation of state and its saturation properties and proceed to the single-nucleon potential. We also explore short-range correlations as seen through the defect function. The various predictions which we present have a common foundation in an internally consistent ab initio approach.

We explore neutron skin predictions for ${}^{208}\mathrm{Pb}$ in relation to the symmetry pressure in various microscopic models based on realistic nucleon-nucleon potentials and either the Dirac-Brueckner-Hartree-Fock approach or the conventional Brueckner-Hartree-Fock framework implemented with three-body forces. We also discuss the correlation between the neutron skin and the radius of a fixed-mass neutron star.

We present predictions for the neutron matter equation of state, from leading to fourth order of chiral effective field theory, using recently developed, accurate chiral nucleon-nucleon potentials. For the many-body method, we employ the nonperturbative particle-particle ladder approximation, that is, we solve the $G$-matrix equation. We find the impact of subleading three-neutron forces to be mild and attractive. We also show order-by-order predictions for the symmetry energy, and discuss its density dependence in relation to empirical constraints. For the nuclear matter equation of state, in this work we adopt an empirical parametrization with good saturation properties. This is to highlight, specifically, the energy and pressure in neutron matter, particularly when comparing with empirical constraints.