Quark matter or QCD matter (quantum chromodynamic) refers to any of a number of hypothetical phases of matter whose degrees of freedom include quarks and gluons, of which the prominent example is quark-gluon plasma. Several series of conferences in 2019, 2020, and 2021 were devoted to this topic. Quarks are liberated into quark matter at extremely high temperatures and/or densities, and some of them are still only theoretical as they require conditions so extreme that they cannot be produced in any laboratory, especially not at equilibrium conditions. Under these extreme conditions, the familiar structure of matter, where the basic constituents are nuclei (consisting of nucleons which are bound states of quarks) and electrons, is disrupted. In quark matter it is more appropriate to treat the quarks themselves as the basic degrees of freedom. In the standard model of particle physics, the strong force is described by the theory of QCD. At ordinary temperatures or densities this force just confines the quarks into composite particles (hadrons) of size around 10−15 m = 1 femtometer = 1 fm (corresponding to the QCD energy scale ΛQCD ≈ 200 MeV) and its effects are not noticeable at longer distances. However, when the temperature reaches the QCD energy scale (T of order 1012 kelvins) or the density rises to the point where the average inter-quark separation is less than 1 fm (quark chemical potential μ around 400 MeV), the hadrons are melted into their constituent quarks, and the strong interaction becomes the dominant feature of the physics. Such phases are called quark matter or QCD matter. The strength of the color force makes the properties of quark matter unlike gas or plasma, instead leading to a state of matter more reminiscent of a liquid. At high densities, quark matter is a Fermi liquid, but is predicted to exhibit color superconductivity at high densities and temperatures below 1012 K. Occurrence Natural occurrence According to the Big Bang theory, in the early universe at high temperatures when the universe was only a few tens of microseconds old, the phase of matter took the form of a hot phase of quark matter called the quark–gluon plasma (QGP). Compact stars (neutron stars). A neutron star is much cooler than 1012 K, but gravitational collapse has compressed it to such high densities, that it is reasonable to surmise that quark matter may exist in the core. Compact stars composed mostly