Continuum strong QCD is the application of models and continuum quantum fie
ld theory to the study of phenomena in hadronic physics, which includes; e.
g., the spectrum of QCD bound states and their interactions; and the transi
tion to, and properties of, a quark gluon plasma. We provide a contemporary
perspective, couched primarily in terms of the Dyson-Schwinger equations b
ut also making comparisons with other approaches and models. Our discourse
provides a practitioners' guide to features of the Dyson-Schwinger equation
s [such as confinement and dynamical chiral symmetry breaking] and canvasse
s phenomenological applications to light meson and baryon properties in col
d, sparse QCD. These provide the foundation for an extension to hot, dense
QCD, which is probed via the introduction of the intensive thermodynamic va
riables: chemical potential and temperature. We describe order parameters w
hose evolution signals deconfinement and chiral symmetry restoration, and c
hronicle their use in demarcating the quark gluon plasma phase boundary and
characterising the plasma's properties. Hadron traits change in an equilib
rated plasma. We exemplify this and discuss putative signals of the effects
. Finally, since plasma formation is not an equilibrium process, we discuss
recent developments in kinetic theory and its application to describing th
e evolution from a relativistic heavy ion collision to an equilibrated quar
k gluon plasma.