The discovery of high-energy cosmic neutrinos opened a new window of astroparticle physics. Their origin is a new mystery in the field, which is tightly connected to the long-standing puzzle about the origin of cosmic rays. I will discuss theoretical implications of the latest results on high-energy neutrino and cosmic-ray observations, and demonstrate the power of multi-messenger approaches. In particular, I will show that the observed fluxes of neutrinos, gamma rays, and extragalactic cosmic rays can be understood in a unified manner. I will also highlight our recent developments about astrophysical neutrino emission from gamma-ray dark sources and violent transient phenomena such as supermassive black hole flares. I may discuss some possibilities of utilizing high-energy neutrinos as a probe of physics beyond the Standard Model.