  A fundamental question of physics is what ultimately happens to matter as it
is heated or compressed. In the realm of very high temperature and density the
fundamental degrees of freedom of the strong interaction, quarks and gluons,
come into play and a transition from matter consisting of confined baryons and
mesons to a state with 'liberated' quarks and gluons is expected. The study of
the possible phases of strongly-interacting matter is at the focus of many
research activities worldwide. In this article we discuss physical aspects of
the phase diagram, its relation to the evolution of the early universe as well
as the inner core of neutron stars. We also summarize recent progress in the
experimental study of hadronic or quark-gluon matter under extreme conditions
with ultrarelativistic nucleus-nucleus collisions.
