Recent advances in novel technologies such as chirped pulse amplificat
ion and high gradient rf photoinjectors make it possible to study expe
rimentally the interaction of relativistic electrons with ultrahigh in
tensity photon fields. Femtosecond laser systems operating in the TW-P
W range are now available, as well as synchronized relativistic electr
on bunches with subpicosecond durations and THz bandwidths. Ponderomot
ive scattering can accelerate these electrons with extremely high grad
ients in a three-dimensional vacuum laser focus. The nonlinear Doppler
shift induced by relativistic radiation pressure in Compton backscatt
ering is shown to yield complex nonlinear spectra which can be modifie
d by using temporal laser pulse shaping techniques. Colliding lasers p
ulses, where ponderomotive acceleration and Compton backscattering are
combined, could also yield extremely short wavelength photons. Finall
y, strong radiative corrections are expected when the Doppler-upshifte
d laser wavelength approaches the Compton scale. These are discussed w
ithin the context of high field classical electrodynamics, a new disci
pline borne out of the aforementioned innovations. (C) 1998 American I
nstitute of Physics.