The strong interaction described by quantum chromodynamics gives rise to the formation of hadrons and nuclei that constitute the baryonic matter in the universe and governs the densest matter in neutron stars and highest temperatures reached in compact object mergers. On the theoretical side, there are impressive advances towards a unified description of all nuclei and matter based on effective field theories of the strong interaction combined with powerful many-body methods. At the same time, neutron-rich nuclei and neutron-rich matter are being explored in new experimental facilities worldwide, as well as from astrophysics, with the discovery of neutron star mergers, observations of heavy neutron stars, and constraints on neutron star radii from NICER. In this colloquium, we will discuss the advances and challenges in understanding and predicting strong interaction matter, with a focus on matter at neutron-rich extremes.