The synergy of GLAST and the proposed EXIST mission as the Black Hole Finder Probe in the Beyond Einstein Program is remarkable. With its full-sky per orbit hard X-ray imaging (3-600 keV) and nuFnu sensitivity comparable to GLAST, EXIST could measure variability and spectra of Blazars in the hard X-ray synchrotron component simultaneous with GLAST (~10-100GeV) measures of the inverse Compton component, thereby uniquely constraining intrinsic source spectra and allowing measured high energy spectral breaks to measure the cosmic diffuse extra-galactic background light (EBL) by determining the intervening diffuse IR photon field required to yield the observed break from photon-photon absorption. Such studies also constrain the physics of jets (and parameters and indeed the validity of SSC models) and the origin of the >100 MeV gamma-ray diffuse background likely arising from Blazars and jet-dominated sources. An overview of the EXIST mission, which could fly in the GLAST era, is given together with a synopsis of other key synergies of GLAST-EXIST science.