I will review models of possible origin of the all-sky astrophysical neutrino signal in the energy range 0.01-10 PeV detected by IceCube and discuss its connection to the all-sky gamma-ray signal measured by Fermi telescope in the TeV band. I will show that consistency of the Fermi and IceCube all-sky spectra indicate the presence of nearby (Galactic neutrino source(s) contribution to the neutrino signal in sub-PeV range. At the same time, I will show that a possibility that hard multi-PeV neutrino signal is explained by population of distant blazars, in spite of the absence of correlation of neutrino arrival directions with positions of known gamma-ray emitting sources of this class.