  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.
