  Evidence for an accelerated expansion of the universe as it has been revealed
ten years ago by the Hubble diagram of distant type Ia supernovae represents
one of the major modern revolutions for fundamental physics and cosmology. It
is yet unclear whether the explanation of the fact that gravity becomes
repulsive on large scales should be found within general relativity or within a
new theory of gravitation. However, existing evidences for this acceleration
all come from astrophysical observations. Before accepting a drastic revision
of fundamental physics, it is interesting to critically examine the present
situation of the astrophysical observations and the possible limitation in
their interpretation. In this review, the main various observational probes are
presented as well as the framework to interpret them with special attention to
the complex astrophysics and theoretical hypotheses that may limit actual
evidences for the acceleration of the expansion. Even when scrutinized with
sceptical eyes, the evidence for an accelerating universe is robust.
Investigation of its very origin appears as the most fascinating challenge of
modern physics.
