We will summarize how future measurements of electromagnetic probes at the upgraded Relativistic Heavy Ion Collider (RHIC-II), in connection with theoretical analysis, can advance our understanding of strongly interacting matter at high energy densities and temperatures. Electromagnetic probes have already played a very important role at SPS and RHIC to date. We will try to identify key physics objectives and observables that remain to be addressed. These include measuring the initial temperature and examining the transition properties via continuum radiation, studying the energy loss mechanism in the medium, the system size evolution via photon-photon correlations as well as medium modifications of vector mesons via low-mass dileptons. We will argue that detector upgrades, increased experimental precision, order of magnitude higher statistics than currently achievable, as well as a detailed scan of colliding species and energies are necessary to allow for sufficient discrimination power in theoretical interpretations.