  The Cherenkov Telescope Array (CTA), currently in its Preparatory Phase, will
be the first open observatory for very high energy gamma-rays from galactic and
extragalactic sources. The international consortium behind CTA is preparing the
construction of two large arrays of Cherenkov telescopes in the Northern and
Southern Hemispheres with a performance that will be significantly improved
compared to the current generation of arrays.
  Its increased sensitivity and energy range will give CTA access to a large
population of Active Galactic Nuclei (AGN) not yet detected at very high
energies and provide much more details on known TeV sources. While the low end
of the CTA energy coverage will close the current gap with the Fermi-LAT band,
its high energy coverage will open a new window on the sky and help us
understand the intrinsic shape of the hardest blazar spectra.
  We outline the current status of CTA and discuss the science case for AGN
physics with the observatory. Predictions for source detections based on
extrapolations of Fermi-LAT spectra are discussed. An overview is given of
prospects for the detection of extended emission from radio galaxies, of rapid
variability, and spectral features. The observation of AGN with CTA will also
improve current constraints on the distribution of the extragalactic background
light, the strength of the intergalactic magnetic field and Lorentz invariance
violation.
