The QCD Phase Diagram, Equation of State, and Heavy Ion Collisions

After some historic remarks and a brief summary of recent theoretical news about the QCD phases, we turn to the issue of $freeze-out$ in heavy ion collisions. We argue that the chemical freeze-out line should actually consists of two crossing lines of different nature. We also consider some inelatic reactions which occure $after$ chemical freeze-out, emphasizing the role of overpopulation of pions. The $hydrodynamics$ (with or without hadronic afterburner) explaines SPS/RHIC data on radial and elliptic flow in unexpected details,for different particles, collision energies, and impact parameters. Apart of Equation of State (EoS), it has basically no free parameters. The EoS which describe these data best agrees quite well with the lattice predictions, with the QGP latent heat $\Delta\epsilon\approx 800 Mev/fm^3$. Other phenomena at RHIC, such as ``jet quenching'' and huge ellipticity at large $p_t$, also point toward very rapid entropy production. Its mechanism remains an outstanding open problem: at the end we discuss recent application of the instanton/sphaleron mechanism. The gg collisions with $\sqrt{s}=2-3 GeV$ may result not in mini-jets but rather in production of sphaleron-like gluomagnetic clusters, which are classically unstable and promptly decay into several gluons and quarks, in sperical mini-Bangs.