  For some blazars, the gamma-ray absorption features due to pair-production on
the Extragalactic Background Light (EBL) are fainter than expected. The present
work reviews the main models that could explain this paradox, with emphasis on
conservative ones, that do not include any new physics. The models that are
intrinsic to the source, do allow a very hard primary spectrum, but fail to
explain a regular redshift dependence of the anomaly starting energy. The model
that includes a contribution from secondary photons produced by cosmic rays
(CR) near the Earth seems to require a well collimated CR beam, what is hard to
achieve. Finally, the model with secondary photons produced in electromagnetic
(EM) cascades initiated by primary gamma-rays is considered. In principle, it
allows to decrease the statistical significance of the anomaly and, while
requiring quite low EGMF strength B, does not contradict to most contemporary
constraints on the B value. Additionally, it is shown that the recently
observed correlation between directions to hard gamma-ray sources and voids in
the Large Scale Structure is a natural feature of the EM cascade model.
