The VHE anomaly in blazar spectra and related phenomena

Most of the recent research on extragalactic $\gamma$-ray propagation focused on the study of the $\gamma\gamma \rightarrow e^{+}e^{-}$ absorption process ("absorption-only model"). Starting from a possible anomaly at very high energies (VHE, E >100 GeV), we briefly review several existing deviations from this model. The exotic interpretation of the VHE anomaly is not supported by the recent works. On the other hand, the process of intergalactic electromagnetic cascade development naturally explains these effects. We discuss phenomenology of intergalactic cascades and the main spectral signatures of the electromagnetic cascade model. We also briefly consider the hadronic cascade model; it also may explain the data, but requires low strength of magnetic field around the source of primary protons or nuclei.