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

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