Supernova neutrinos, direct messengers of the core-collapse event, have been studied by many researchers. Diffuse neutrino background from cosmological supernovae is considered to be realistically detectable in the near future. I review recent progress of theoretical and observational studies about this topic, and discuss prospects of future large volume detector era. I also introduce another (more recent) project, i.e. predicting the detectability of supernova neutrinos from nearby (~3 Mpc) galaxies, using the future megaton detectors. Detection of these neutrinos would provide rich information, most importantly for gravitational wave searches.