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The microscopic parton-hadron-string dynamics (PHSD) transport approach describes the full evolution of relativistic heavy-ion collisions: from the initial hard scatterings to the partonic phase in the early hot and dense reaction region (when the local energy density is above 1 GeV/fm 3 ) followed by hadronization and off-shell hadron propagation and interactions. The description of quarks and gluons in PHSD is based on the dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. The DQPM describes QCD properties in terms of single-particle Green’s functions and leads to the notion of effective quasiparticles which are massive and have broad spectral functions (due to large interaction rates). Dressing the quark and gluon lines with effective propagators provided by the DQPM, we obtain cross sections of dilepton production in the reactions q+ ¯ q >l + l (Born mechanism), q+ ¯ q >l + l +g (quark annihilation with the gluon Bremsstrahlung in the final state), and q=¯

Dilepton production at SPS and RHIC energies