Quantum Chromodynamics (QCD), the theory of strong interactions of quarks and gluons within the Standard Model of elementary particles, displays a rich thermodynamics with a variety of phases. At low temperature, the spontaneously broken chiral symmetry of QCD implies the existence of a strong quark-antiquark condensate that governs the physics of hadrons. At high temperature this chiral condensate melts and the hadronic sector undergoes a transition to a phase of deconfined quarks and gluons. At high quark densities and low temperatures, several superconducting phases with condensed diquarks are expected to appear. Last not least, nuclear matter with its liquid-gas phase transition figures prominently in the center of the phase diagram. This colloquium outlines our present understanding of these phenomena. Recent results from Lattice QCD will be highlighted. Empirical constraints from high-energy heavy-ion collisions and from astrophysical observations will also be discussed.