  Ongoing searches for supernovae (SNe) at cosmological distances have recently
started to provide a link between SN Ia statistics and galaxy evolution. In
this talk I will use recent estimates of the global history of star formation
to compute the theoretical Type Ia and Type II SN rates as a function of cosmic
time. I will compare the predicted values with the rates observed in the range
0<z<0.4, and show how accurate measurements of the frequency of SN events at
intermediate redshifts are valuable probes of the evolution of the stellar
birthrate in the universe and the nature of Type Ia progenitors. The Next
Generation Space Telescope should detect of order 20 Type II SNe per field per
year in the interval 1<z<4.
