The extreme luminosity and their fairly unique temporal behaviour have made supernovae a superb tool to measure distances in the universe. As complex astrophysical events they provide interesting insights into explosion physics, explosive nucleosynthesis, hydrodynamics of the explosion and radiation transport. They are an end product of stellar evolution and provide clues to the stellar composition. Since they can be observed at large distances they have become critical probes to further explore astrophysical effects, like dust properties in external galaxies and the star formation history of galaxies. Some of the astrophysics interferes with the cosmological applications of supernovae. The local velocity field, distorted by the gravitational attraction of the local large scale structure, and the reddening law appear at the moment the major limitations in the accuracy with which cosmological parameters can be determined. These absorption effects can introduce a secondary bias into the observations of the distant supernovae, which needs to be carefully evaluated. Supernovae have been used for the measurement of the Hubble constant, i.e. the current expansion rate of the universe, and the accelerated cosmic expansion directly inferred from the apparent faintness of the distant supernovae.