  We show that there is no universal law describing how the spectra and
luminosity of synchrotron and inverse Compton radiation from relativistic jets
change with increasing observation angle. Instead, the physics of particle
acceleration leaves pronounced imprints in the observed spectra and allows for
a freedom in numerous modifications of them. The impact of these effects is the
largest for high-energy radiation and depends on the details of particle
acceleration mechanism(s), what can be used to discriminate between different
models. Generally, the beam patterns of relativistic jets in GeV-TeV spectral
domain are much wider than the inverse Lorentz factor. The off-axis emission in
this energy range appear to be brighter, have much harder spectra and a much
higher cut-off frequency compared to the values derived from Doppler boosting
considerations alone.
  The implications include the possibility to explain high-latitude
unidentified EGRET sources as off-axis but otherwise typical relativistic-jet
sources, such as blazars, and the prediction of GeV-TeV afterglow from
transient jet sources, such as Gamma-Ray Bursts. We also discuss the phenomenon
of beam-pattern broadening in application to neutrino emission.
