It is demonstrated that the field emission from graphene-like structures (GLSs) has a very low excitation threshold (about two orders of magnitude lower than that of metals and semiconductors). It is shown that the total energy distribution (TED) of field emission electrons from GLSs differs considerably from the spectra obtained for metals. The existence of two maxima of this distribution (spaced 0.7-1.7 eV apart), significant broadening of the energy distribution, and a shift of these maxima depending on the electric field intensity are reported. The resonance nature of low-threshold field emission from GLSs is confirmed.