  Over the last 20 years, supernovae have become a key tool to constrain the
expansion history of the Universe through the construction of Hubble diagrams,
using luminosity distances to supernovae belonging to the "Ia" subtype. This
technique was key for the discovery that the expansion of the Universe is now
accelerating. We review the principle and difficulties of the measurements, the
classification and diversity of supernovae, and the physics of the explosion.
We discuss the systematic uncertainties affecting the cosmological conclusions
with some emphasis on photometric calibration. We describe the major supernova
cosmology surveys, the presented analyses and their conclusions, together with
the present status of the field. We conclude on the expectations for the near
future.
