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Since the launch of Chandra twenty years ago, one of the greatest mysteries surrounding Quasar Jets is the production mechanism for their extremely high X-ray luminosity. Two mechanisms have been proposed. In the first view, the X-ray emission is inverse-Comptonized CMB photons. This view requires a jet that is highly relativistic (bulk Lorentz factor >20–40) on scales of hundreds of kiloparsecs, and a jet that is comparably or more powerful than the black hole’s Eddington luminosity. The second possibility is synchrotron emission from a high-energy population of electrons. This requires a much less powerful jet that does not need to be relativistically beamed, but it imposes other extreme requirements, namely the need to accelerate particles to >100 TeV energies at distances of hundreds of kiloparsecs from the active nucleus. We are exploring these questions using a suite of observations from a diverse group of telescopes, including the Hubble Space Telescope (HST), Chandra X-ray Observatory (CXO), Fermi Gamma-ray Space Telescope and various radio telescope arrays. Our results strongly favor the hypothesis that the X-ray emission is synchrotron radiation from a separate, high-energy electron population. We discuss the observations, results and new questions brought up by these surprising results. We investigate the physical processes and magnetic field structure that may help to accelerate particles to such extreme energies.