We present the light-curves and spectra of 24 afterglows that have been monitored by Fermi-LAT at 0.1-100 GeV over more than a decade in time. All light-curves (except 130427) are consistent with a single power-law starting from their peaks, which occurred, in most cases, before the burst end. The light-curves display a brightness-decay rate correlation, with all but one (130427) of the bright afterglows decaying faster than the dimmer afterglows. We attribute this dichotomy to a quick deposition of the relativistic ejecta energy in the external-shock for the brighter/faster-decaying afterglows and to an extended energy-injection in the afterglow shock for the dimmer/slower-decaying light-curves. The spectra of six afterglows (090328, 100414, 110721, 110731, 130427, 140619B) indicate the existence of a harder component above a spectral dip/ankle at energy 0.3-3 GeV, offering evidence for an inverse-Compton emission at higher energies, and suggesting that the harder power-law spectra of five other LAT afterglows (130327B, 131231, 150523, 150627, 160509) could also be inverse-Compton, while the remaining softer LAT afterglows should be synchrotron. Marginal evidence for a spectral break and softening at higher energies is found for two afterglows (090902B and 090926).