PHENIX has measured the dielectron continuum in sqrt(s_(NN))=200 GeV Au+Au and p+p collisions. In minimum bias Au+Au collisions the dielectron yield in the mass range between 150 and 750 MeV/c^2 is enhanced by a factor of 3.4 +/- 0.2(stat.) +/- 1.3(syst.) +/- 0.7(model) compared to the expectation from our model of hadron decays that well reproduces the mass spectrum in p+p collisions. The integrated yield increases faster with the centrality of the collisions than the number of participating nucleons, suggesting emission from scattering processes in the dense medium. The continuum yield between the masses of the phi and the J/psi meson is consistent with expectations from correlated ccbar production, though other mechanisms are not ruled out.