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