Recently, the observational study of gamma-ray bursts (GRBs) in the very-high-energy (VHE) regime has advanced
with several long-awaited detections with MAGIC, H.E.S.S., and LHAASO telescope systems. Currently, the list of GRBs
with robustly measured VHE emissions contains GRB 180720B, GRB 190114C, GRB 190829A and GRB 221009A. Three more
bursts were reported as source candidates by the MAGIC Collaboration. This candidate list includes a short GRB, which
was detected with low significance (GRB 160821B), and a very distant GRB 201216C (from \(z=1.1\)), which was detected
with high significance (\(>5\sigma\)). Detection of GRB afterglows in the VHE regime allows us to obtain essential information on particle acceleration
by relativistic shock waves. This makes GRB afterglows important sources in high-energy astrophysics and their
studies have an exceptionally broad scope. However, the extragalactic origin of GRB implies a severe constraint for
their observational study in the VHE domain. Namely, the attenuation of multi-TeV photons by extragalactic background
light (EBL) becomes significant at cosmological distances. The EBL absorption hardens the detection of GRBs and
deforms their TeV spectrum, making nearly impossible any reliable determination of the intrinsic gamma-ray
spectrum. The fortunate proximity of one of the detected GRBs (GRB 190829A occurred at \(z\approx0.08\)) allowed an
unexpectedly long signal detection, up to 56 hours after the trigger, and an accurate (and nearly independent on the specific EBL model) spectral determination in a broad
energy interval, spanning from 0.18 to 3.3~TeV. The temporal and spectral properties of the VHE emission
appeared to be remarkably similar to those seen in the X-ray band with Swift-XRT. Comparison to other detected GRB
afterglow shows that SEDs and lightcurves obtained from GRBs share much in common. This disfavors the chances for GRB
190829A being an exceptional event, thus this case can be used as a standard event for testing afterglow models. Since many of the theoretical and numerical models fail to reproduce the hard powerlaw spectrum detected from \grbHII, this result may demand the need for a new generation of models used to predict
the broadband emission from the GRB afterglows.