Deconfinement and hadron properties at extremes of temperature and density

After introducing essential, qualitative concepts and results, we discuss the application of Dyson-Schwinger equations to QCD at finite T and mu. We summarise the calculation of the critical exponents of two-light-flavour QCD using the chiral and thermal susceptibilities; and an algebraic model that elucidates the origin of an anticorrelation between the mu- and T-dependence of a range of meson properties. That model also provides an algebraic understanding of why the finite-T behaviour of bulk thermodynamic properties is mirrored in their mu-dependence, and why meson masses decrease with mu even though f(pi) and -[(q) over bar q] increase. The possibility of diquark condensation is canvassed. Its realisation is uncertain because it is contingent upon an assumption about the quark-quark scattering kernel that is demonstrably false in some applications; e.g., it predicts the existence of coloured diquarks in the strong interaction spectrum, which are not observed.