  We review the potential of precise measurements of electromagnetic probes in
relativistic heavy-ion collisions for the theoretical understanding of strongly
interacting matter. The penetrating nature of photons and dileptons implies
that they can carry undistorted information about the hot and dense regions of
the fireballs formed in these reactions and thus provide a unique opportunity
to measure the electromagnetic spectral function of QCD matter as a function of
both invariant mass and momentum. In particular we report on recent progress on
how the medium modifications of the (dominant) isovector part of the vector
current correlator ($\rho$ channel) can shed light on the mechanism of chiral
symmetry restoration in the hot and/or dense environment. In addition, thermal
dilepton radiation enables novel access to (a) the fireball lifetime through
the dilepton yield in the low invariant-mass window $0.3 \; \mathrm{GeV} \leq M
\leq 0.7 \; \mathrm{GeV}$, and (b) the early temperatures of the fireball
through the slope of the invariant-mass spectrum in the intermediate-mass
region ($1.5 \; \mathrm{GeV} <M< 2.5 \; \mathrm{GeV}$). The investigation of
the pertinent excitation function suggests that the beam energies provided by
the NICA and FAIR projects are in a promising range for a potential discovery
of the onset of a first order phase transition, as signaled by a non-monotonous
behavior of both low-mass yields and temperature slopes.
