  Gamma-ray bursts (GRBs) are fascinating extragalactic objects. They represent
a fantastic opportunity to investigate unique properties not exhibited in other
sources. Multi-wavelength afterglow observations from some short- and
long-duration GRBs reveal an atypical long-lasting emission that evolves
differently from the canonical afterglow light curves favoring the off-axis
emission. We present an analytical synchrotron afterglow scenario, and the
hydrodynamical evolution of an off-axis top-hat jet decelerated in a stratified
surrounding environment. The analytical synchrotron afterglow model is shown
during the coasting, deceleration (off- and on-axis emission), and the
post-jet-break decay phases, and the hydrodynamical evolution is computed by
numerical simulations showing the time evolution of the Doppler factor, the
half-opening angle, the bulk Lorentz factor, and the deceleration radius. We
show that numerical simulations are in good agreement with those derived with
our analytical approach. We apply the current synchrotron model and describe
successfully the delayed non-thermal emission observed in a sample of long and
short GRBs with evidence of off-axis emission. Furthermore, we provide
constraints on the possible afterglow emission by requiring the
multi-wavelength upper limits derived for the closest Swift-detected GRBs and
promising gravitational-wave events.
