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In this review we address the dynamics of relativistic heavy-ion reactionsand in particular the information obtained from electromagnetic probes thatstem from the partonic and hadronic phases. The out-of-equilibrium descriptionof strongly interacting relativistic fields is based on the theory of Kadanoffand Baym. For the modeling of the partonic phase we introduce a dynamicalquasiparticle model (DQPM) for QCD in equilibrium. The widths and masses of thequasiparticles are controlled by transport coefficients in comparison tolattice QCD results. The resulting off-shell transport approach - denoted byParton-Hadron-String Dynamics (PHSD) - also includes covariant dynamicalhadronization and keeps track of the hadronic interactions in the final phase.We show that PHSD captures the bulk dynamics of heavy-ion collisions from SPSto LHC energies and provides a basis for the evaluation of the electromagneticemissivity, using the same dynamical parton propagators as for the systemevolution. Direct photon production in elementary processes and heavy-ionreactions at RHIC and LHC energies is investigated and the status of the photonv2 puzzle - a large elliptic flow of the direct photons observed in A+Acollisions - is addressed. We discuss the roles of hadronic and partonicsources for the photon spectra and the flow coefficients v2 and v3 and also thepossibility to subtract the QGP signal from observables. Furthermore, theproduction of dilepton pairs is addressed from SIS to LHC energies. Thelow-mass dilepton yield is enhanced due to the in-medium modification of therho-meson and at the lowest energy also due to a multiple regeneration ofDelta-resonances. In addition, a signal of the partonic degrees-of-freedom isfound in the intermediate dilepton mass regime (1.2GeV<M<3GeV), which can shedlight on the nature of the very early degrees-of-freedom in nucleus-nucleuscollisions.

Effective QCD and transport description of dilepton and photon production in heavy-ion collisions and elementary processes