Testing models of extragalactic $gamma$-ray propagation using observations of extreme blazars in GeV and TeV energy ranges

We briefly review contemporary extragalactic {gamma}-ray propagation models. It is shown that the Extragalactic Magnetic Field (EGMF) strength and structure are poorly known. Strict lower limits on the EGMF strength in voids are of order 10^{-17}--10^{-20} G, thus allowing a substantial contribution of a secondary component generated by electromagnetic cascades to the observable spectrum. We show that this electromagnetic cascade model is supported by data from imaging Cherenkov telescopes and the Fermi LAT detector.