An important guiding theme of modern nuclear, particle and astrophysics is the exploration of the phases emerging from the Strong Interaction within the Standard Model of elementary particles: from quarks and gluons to the formation of composite structures such as nucleons and nuclei, including the dynamical generation of their masses. The starting point and well established theoretical framework for this research area is Quantum Chromodynamics (QCD), its symmetries and symmetry breaking scenarios. This colloquium describes how such symmetry principles are at the origin of effective field theories that establish the interface e.g. between QCD and nuclear physics. Phase transitions of strongly interacting matter are discussed in this context, and it is demonstrated how such a theoretical framework confronts large varieties of empirical data. The presentation ends with new results and constraints concerning properties of highly compressed baryonic matter in the center of neutron stars.