The observations of the exceptionally bright gamma-ray burst (GRB) 130427A by the Large Area Telescope aboard the Fermi Gamma-ray Space Telescope provide constraints on the nature of such unique astrophysical sources. GRB 130427A had the largest fluence, highest-energy photon (95 GeV), longest \(\gamma\)-ray duration (20 hours), and one of the largest isotropic energy releases ever observed from a GRB. Temporal and spectral analyses of GRB 130427A challenge the widely accepted model that the non-thermal high-energy emission in the afterglow phase of GRBs is synchrotron emission radiated by electrons accelerated at an external shock.