  We review known and discuss new signatures of high-intensity Compton
scattering assuming a scenario where a high-power laser is brought into
collision with an electron beam. At high intensities one expects to see a
substantial red-shift of the usual kinematic Compton edge of the photon
spectrum caused by the large, intensity dependent, effective mass of the
electrons within the laser beam. Emission rates acquire their global maximum at
this edge while neighbouring smaller peaks signal higher harmonics. In
addition, we find that the notion of the centre-of-mass frame for a given
harmonic becomes intensity dependent. Tuning the intensity then effectively
amounts to changing the frame of reference, going continuously from inverse to
ordinary Compton scattering with the centre-of-mass kinematics defining the
transition point between the two.
