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Intergalactic gamma-ray propagation studies may, in principle, reveal new physics processes such as gamma-axion like particle oscillation, and allow to measure the extragalactic background light (EBL) and extragalactic magnetic field (EGMF). We review several extragalactic gamma-ray propagation models, namely: the absorption-only model (which includes only the pair production process and adiabatic losses), the electromagnetic cascade model (ECM, which includes also inverse Compton and deflection of secondary electrons in the EGMF), and the hadronic cascade model (HCM, which allows for primary protons or nuclei). The absorption-only model is presently under attack as there are several “anomalies” that could not be accomodated in this framework. The ECM and HCM are not excluded at present. We show that source variability will be the critical test for the case of the ECM, and the HCM could be severely constrained if the EGMF structure is known. Finally, for the case of the ECM and the HCM we predict various quantities that could be measured in future with the Cherenkov Telescope array (CTA) observatory.