Type Ia supernovae provide a precise luminosity distance at redshift as high as z 2. At present nearly 200 SN Ia paint a consistent picture that Omega(Lambda) - 1.4 Omega(M) = 0.35 +/- 0.14 (if omega = - 1). If Omega(T) = 1, SN Ia tell us Omega(M) = 0.28 +/- 0.05, independent of any other measurements. Adopting a prior based on the 2dF redshift survey constraint on Omega(M) and assuming a. at universe, then -148 < omega < -0.72 at 95% confidence. If we further assume that omega > -1, we obtain omega < -0.73 at 95% confidence. Understanding systematic errors is of paramount importance, both because they may affect our present results and they will limit the eventual precision achievable. Possible sources of error include photometric error, dust extinction, evolution of SN Ia, selection effects, K-corrections, and gravitational lensing, all which could vary with redshift. There are many efforts underway to push to higher redshift and to control possible observational systematic errors; the bottom line is that the acceleration reported earlier appears to be confirmed. The propagation of systematic error in luminosity distance to inferred w or w( z) depends critically on how much is known about Omega(M). For example, at fixed Omega(M) a systematic uncertainty in d(lum) of 0.04mag corresponds to a 10% uncertainty in w, but this becomes much worse if Omega(M) is not known. We will have some good constraints on Omega(M), either directly from 2dF or SDSS, or indirectly from WMAP whose constraints in the (Omega(M), w) plane run more or less perpendicular to the SN Ia (but they can also have systematic errors themselves). Theoretical models for SN Ia are now able to make multi-wavelength light curves and spectra which are a decent match to observation. The luminosity-decline rate correlation depends primarily on the amount of Ni-56 produced in the explosion. There are other, more subtle effects which are also being elucidated, for example, increasing initial metallicity (in the form of neutron-rich Fe-56 and Fe-22) diminishes the neutron-poor Ni-56 and dims the explosion. Unfortunately we have very little idea at present about what causes a WD to explode. A small fraction of WD explode, and those that do wait a long time between their formation and their explosion. Without initial conditions, there is a lot of room for systematic error at the 0.02 mag level from SN Ia explosions, and whether they depend in a serious way with z and therefore limit our ability to measure w( z) remains to be seen. It may be that we can measure d(lum)(z) to 1% (0.02 mag) by controlling only observational systematics, or it may be that we incur significant systematic errors for which we do not have the requisite information to realize their presence or correct for them.
