Melting Hadrons, Boiling Quarks

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. Finally in two appendices I present previously unpublished reports describing the early prediction of the different forms of hadron matter and of the formation of QGP in relativistic heavy ion collisions, including the initial prediction of strangeness and in particular strange antibaryon signature of QGP.