Dileptons and hadron spectral functions in heavy-ion collisions

We briefly review the dilepton experiments at BEVALAC/SIS and SPS energies for p+p, p+A and A+A collisions as well as our present understanding of the data within transport theoretical simulations. Since dileptons from p+A and A+A collisions in particular probe the in-medium spectral functions of vector mesons, a novel semiclassical off-shell transport approach is introduced on the basis of the Kadanoff-Baym equations that describes the dynamical evolution of broad hadron spectral functions. The implications of the off-shell dynamics -- relative to the conventional on-shell transport dynamics -- are discussed for proton spectra, high energy $\gamma$, pion, kaon and antikaon production from GANIL to AGS energies in comparison to experimental data.