  We review the impact of nuclear forces on matter at neutron-rich extremes.
Recent results have shown that neutron-rich nuclei become increasingly
sensitive to three-nucleon forces, which are at the forefront of theoretical
developments based on effective field theories of quantum chromodynamics. This
includes the formation of shell structure, the spectroscopy of exotic nuclei,
and the location of the neutron dripline. Nuclear forces also constrain the
properties of neutron-rich matter, including the neutron skin, the symmetry
energy, and the structure of neutron stars. We first review our understanding
of three-nucleon forces and show how chiral effective field theory makes unique
predictions for many-body forces. Then, we survey results with three-nucleon
forces in neutron-rich oxygen and calcium isotopes and neutron-rich matter,
which have been explored with a range of many-body methods. Three-nucleon
forces therefore provide an exciting link between theoretical, experimental and
observational nuclear physics frontiers.
