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The High Energy Stereoscopic System (H.E.S.S.) experiment, a ground-basedgamma-ray Cherenkov telescope array located in Namibia, has now detected manyextragalactic objects, which redshifts range from z=0.00183 up to z=0.2,possibly more. With the increasing performances of Cherenkov telescopes, it nowbecomes possible to probe these objects at small timescales in gamma-ray,allowing the study of regions thought to be very close to the centralsupermassive black holes. Furthermore, H.E.S.S. has confirmed a gamma-rayemission from M87, which is thus the first extragalactic source seen at the TeVrange that is not a blazar.  Among blazars, TeV BL Lacs are the most challenging objects to test the jetemission models and to shed light on particle acceleration mechanisms. Thestudy of blazars with H.E.S.S. also revealed various temporal behaviors amongthem. Some objects presents a highly variable X-ray flux with small variationof the gamma-ray, while others show the inverse behavior. The interpretation ofsuch differences is puzzling.  Observations at very high energies also bring indirect measurements of theinfrared extragalactic background light (EBL). The interpretation of gamma-rayemission of radiogalaxies such as M87 in terms of misaligned blazars and theunderstanding of the properties of the EBL represent new challenges brought byH.E.S.S. observations of extragalactic sources.

Multiwavelength modeling of TeV AGN observed by HESS