  A critical discussion of the present signals for the phase transition to
quark-gluon plasma (QGP) is given. Since hadronic rescattering models predict
much larger flow than observed from 1 to 50 A GeV laboratory bombarding
energies, this observation is interpreted as potential evidence for a
first-order phase transition at high baryon density. A detailed discussion of
the collective flow as a barometer for the equation of state (EoS) of hot dense
matter at RHIC follows. Here, hadronic rescattering models can explain < 30 %
of the observed elliptic flow v_2 for $p_T > 2$ GeV/c. This is interpreted as
an evidence for the production of superdense matter at RHIC. The connection of
v_2 to jet suppression is examined. A study of Mach shocks generated by fast
partonic jets propagating through the QGP is given. The main goal is to take
into account different types of collective motion during the formation and
evolution of this matter. A significant deformation of Mach shocks in central
Au+Au collisions at RHIC and LHC energies as compared to the case of jet
propagation in a static medium is predicted. A new hydrodynamical study of jet
energy loss is presented.
