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ABSTRACT The afterglow emission from gamma-ray bursts (GRBs) is believed to originate from a relativistic blast wave driven into the circumburst medium. Although the afterglow emission from radio up to X-ray frequencies is thought to originate from synchrotron radiation emitted by relativistic, non-thermal electrons accelerated by the blast wave, the origin of the emission at high energies (HE; ≳GeV) remains uncertain. The recent detection of sub-TeV emission from GRB 190114C by the Major Atmospheric Gamma Imaging Cherenkov Telescopes (MAGIC) raises further debate on what powers the very high energy (VHE; ≳300 GeV) emission. Here, we explore the inverse Compton scenario as a candidate for the HE and VHE emissions, considering two sources of seed photons for scattering: synchrotron photons from the blast wave (synchrotron self-Compton or SSC) and isotropic photon fields external to the blast wave (external Compton). For each case, we compute the multiwavelength afterglow spectra and light curves. We find that SSC will dominate particle cooling and the GeV emission, unless a dense ambient infrared photon field, typical of star-forming regions, is present. Additionally, considering the extragalactic background light attenuation, we discuss the detectability of VHE afterglows by existing and future gamma-ray instruments for a wide range of model parameters. Studying GRB 190114C, we find that its afterglow emission in the Fermi-Large Area Telescope (LAT) band is synchrotron dominated. The late-time Fermi-LAT measurement (i.e. t ∼ 104 s), and the MAGIC observation also set an upper limit on the energy density of a putative external infrared photon field (i.e. $${\lesssim} 3\times 10^{-9}\, {\rm erg\, cm^{-3}}$$), making the inverse Compton dominant in the sub-TeV energies.