Abstract: Recently, the observational study of gamma-ray bursts (GRBs) in the very-high-energy (VHE) regime has advanced with several long-awaited detection with MAGIC, H.E.S.S., and LHAASO telescope systems. Currently, the list of GRBs with VHE emission measured with very high significance (5 sigma) contains GRB 190114C, GRB 190829A, and GRB 221009A. Several more bursts were detected with lower significance or reported as source candidates.
Detection of GRB afterglows in the VHE regime allows obtaining essential information on particle acceleration by relativistic shock waves. This makes GRB afterglows to be important sources for high-energy astrophysics and their studies have an exceptionally broad scope. Two detected GRBs provided us with exceptionally viable data because of the proximity (GRB 190829A) and record-breaking luminosity (GRB 221009A). In this case, Cherenkov detectors provide us with detailed spectral information and well-measured light curves. In the former case, one H.E.S.S. GRB revealed anunexpectedly long signal duration, up to 56 hours after the trigger, and accurately measured the spectrum in a relatively broad energy interval, spanning between 0.18 and 3.3TeV. From the latter GRB, LHAASO detected more than 60,000 photons during the onset of the afterglow, which resulted in unprecedentedly accurate measurement of the light curve and VHE spectrum, which extends beyond 10 TeV. The obtained temporal and spectral properties of the VHE emission challenged the earlier prediction and promoted further development of existing models and formulation of new approaches. In this talk and will review the key observational findings and developments in the modeling.