Neutrinos play a very important role in multimessenger astronomy. In this talk, I start with a simple argument on how bright the Universe is in both photons and neutrinos. It is remarkable that one can easily show that the neutrinos, especially those emitted from past core-collapse supernovae, form the brightest radiation component in the Universe, ever emitted from astrophysical sources. The detection of this cosmic supernova neutrino background has not been made yet, but is almost guaranteed in the near future. Thus, I review theoretical predictions of the supernova neutrino background, and the latest upper limits experimentally obtained on its flux. Then I discuss prospects of detecting supernova neutrinos from nearby galaxies. With upcoming Mton detectors, or hopefully with a multi-Mton detector, one could study not only supernova neutrinos but also a true stellar death rate, hidden black-hole formation, etc. Finally, I discuss detectability of high-energy neutrinos and implications for underlying supernova–gamma-ray burst connection. Detecting neutrinos will not only give unique diagnostics but also help find gravitational waves.