Type Ia Supernova Cosmology

The primary agent for Type Ia supernova cosmology is the uniformity of their appearance. We present the current status, achievements and uncertainties. The Hubble constant and the expansion history of the universe are key measurements provided by Type Ia supernovae. They were also instrumental in showing time dilation, which is a direct observational signature of expansion. Connections to explosion physics are made in the context of potential improvements of the quality of Type Ia supernovae as distance indicators. The coming years will see large efforts to use Type Ia supernovae to characterise dark energy.