A Review of the High-Redshift Supernovae

6 pages, 2 figures, to appear in "Fundamental Parameters in Cosmology," proceedings of the XXXIIIrd Rencontres de Moriond 1998Observations show that Type Ia Supernovae (SNe Ia) form a homogeneous class of objects. They share similar spectroscopic evolution, light-curve shapes, and peak absolute magnitudes. The slight departures from homogeneity that are observed can be used to produce a "calibrated candle" with corrected magnitudes with even smaller dispersion. The existence of this intrinsically bright distance indicator has inspired two coordinated high-redshift supernova searches: the Supernova Cosmology Project and the High-z Supernova Search Team. To date ~100 SNe Ia have been discovered by the two groups. The preliminary analysis of the first of these objects demonstrate how well SNe Ia can be used to measure the mass density of the universe Omega_M and the normalized cosmological constant Omega_Lambda = Lambda/3H_0^2