For this project, the diffuse supernova neutrino background (DSNB) has been calculated based on the recent direct supernova rate measurements and neutrino spectrum from SN1987A. The estimated diffuse electron antineutrino flux is ∼ 0.10 – 0.59 /cm2/s at 99% confidence level, which is 5 times lower than the Super-Kamiokande 2012 upper limit of 3.0 /cm2/s, above energy threshold of 17.3 MeV. With a Megaton scale water detector, 40 events could be detected above the threshold per year. In addition, the detectability of neutrino bursts from direct black hole forming collapses (failed supernovae) at Megaton detectors is calculated. These neutrino bursts are energetic and with short time duration, ∼ 1s. They could be identified by the time coincidence of N ≥2 or N ≥3 events within 1s time window from nearby (4 – 5 Mpc) failed supernovae. The detection rate of these neutrino bursts could get up to one per decade. This is a realistic way to detect a failed supernova and gives a promising method for studying the physics of direct black hole formation mechanism. Finally, the absorption of ultra high energy (UHE) neutrinos by the cosmic neutrino background, with full inclusion of the effect of the thermal distribution of the background on the resonant annihilation channel, is discussed. Results are applied to serval models of UHE neutrino sources. Suppression effects are strong for sources that extend beyond z ∼ 10. This provides a fascinating probe of the physics of the relic neutrino background in the unexplored redshift interval z ∼ 10 – 100. Ultimately this research will examine the detectability of DSNB, neutrino bursts from failed supernovae and absorption effects in the neutrino spectrum.