Supernova rates: A cosmic history

We discuss the cosmic history of supernovae on the basis of various assumptions and recent data on the star formation history. We show that supernovae rates as a function of redshift can be used to place significant constraints on progenitor models, on the star formation history, and on the importance of dust obscuration. We demonstrate that it is unlikely that the current observational indications for the existence of a cosmological constant are merely an artifact of the dominance of different progenitor classes at different redshift intervals.