In 2013, the IceCube Neutrino Observatory, located at the South Pole, discovered a flux of astrophysical neutrinos with PeV energies, later found to extend down to at least approximately 10 TeV. Despite many efforts since then, determining their sources remains one of the most daunting challenges in the astrophysics community. In this dissertation, we investigate possible sources via a well-motivated multimessenger approach. In any production mechanism of cosmic neutrinos, there must also be a simultaneous production of gamma-rays withcomparable energies. Unlike neutrinos, which travel unscathed throughout the Universe, high energy gamma-rays undergo interactions with background photons in an energy-degrading process known as electromagnetic cascade. At the Earth, they constitute the diffuse extragalactic gamma-ray background (EGB), precisely measured by the Fermi Gamma-ray Space Telescope in the GeV–TeV range. By performing a conservative, quantitative, multimessenger analysis, we find greater than a or approximately to 3 delta (possibly as large as approximately 5 delta) tension between IceCube and EGB data, pointing towards the existence of a new class of high energy cosmic accelerators, such as gamma-ray-opaque sources.