Transport properties of the hot quark-gluon plasma

A phase where quark and gluon are the relevant degrees of freedom is expected for nuclear matter at energy density epsilon >= 1 GeV/fm(3) and a temperature T > 160 MeV. A transient state state of such a matter can be created by mean of ultra-relativistic heavy-ion collisions. We briefly overview some main results on the properties of the quark-gluon plasma emphasizing the necessity to develop a transport theory for quarks and gluons able to incorporate the main developments in lattice QCD and perturbative QCD. First results show that Boltzmann-Vlasov transport theory correctly predict the elliptic flow observed at both RHIC and LHC energies.