Clear signs of excess dileptons above the known sources were found at the SPS over past years. However, a real clarification of these observations was only recently achieved by NA60, measuring dimuons with unprecedented precision in 158A GeV In-In collisions. The excess mass spectrum in the region M < 1 GeV is consistent with a dominant contribution from pi(+)pi(-) -> rho -> mu(+)mu(-) annihilation. The associated rho spectral function shows a strong broadening, but essentially no shift in mass. In the region M > 1 GeV, the excess is found to be prompt, not due to enhanced charm production. The inverse slope parameter T-eff associated with the transverse momentum spectra rises with mass up to rho, followed by a sudden decline above. While the initial rise, coupled to a hierarchy in hadron freeze-out, points to the radial flow of a hadronic decay source, the decline above signals a transition to a low-flow source, presumably of partonic origin. The mass spectra show at low transverse momenta the steep rise toward low masses, characteristic for Planck-like radiation. The polarization of the excess referred to the Collins Soper frame is found to be isotropic. All observations are consistent with the interpretation of the excess as thermal radiation.