  In the context of the Hagedorn temperature half-centenary I describe our
understanding of the hot phases of hadronic matter both below and above the
Hagedorn temperature. The first part of the review addresses many frequently
posed questions about properties of hadronic matter in different phases, phase
transition and the exploration of quark-gluon plasma (QGP). The historical
context of the discovery of QGP is shown and the role of strangeness and
strange antibaryon signature of QGP illustrated. In the second part I discuss
the corresponding theoretical ideas and show how experimental results can be
used to describe the properties of QGP at hadronization. The material of this
review is complemented by two early and unpublished reports containing the
prediction of the different forms of hadron matter, and of the formation of QGP
in relativistic heavy ion collisions, including the discussion of strangeness,
and in particular strange antibaryon signature of QGP.
