In this paper, we review the prospects for studies of active galactic nuclei (AGN) using the envisioned future Cherenkov Telescope Array (CTA). This review focuses on jetted AGN, which constitute the vast majority of AGN detected at gamma-ray energies. Future progress will be driven by the planned lower energy threshold for very high energy (VHE) gamma-ray detections to ~10 GeV and improved flux sensitivity compared to current-generation Cherenkov Telescope facilities. We argue that CTA will enable substantial progress on gamma-ray population studies by deepening existing surveys both through increased flux sensitivity and by improving the chances of detecting a larger number of low-frequency peaked blazars because of the lower energy threshold. More detailed studies of the VHE gamma-ray spectral shape and variability might furthermore yield insight into unsolved questions concerning jet formation and composition, the acceleration of particles within relativistic jets, and the microphysics of the radiation mechanisms leading to the observable high-energy emission. The broad energy range covered by CTA includes energies where gamma-rays are unaffected from absorption while propagating in the extragalactic background light (EBL), and extends to an energy regime where VHE spectra are strongly distorted. This will help to reduce systematic effects in the spectra from different instruments, leading to a more reliable EBL determination, and hence will make it possible to constrain blazar models up to the highest energies with less ambiguity.
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