Relativistic effects arise when atoms interact with ultrastrong laser
fields. Such effects are expected to become important when the ratio of the
ponderomotive energy Up of an electron in the field to the electron rest
mass energy becomes comparable to unity. In atomic units, this ratio is
Up/c^2=E_0^2/(4 w^2 c^2), where
E_0 is the
peak strength of the electric field,
w is the angular frequency of the
laser light and c is the velocity of light. We discuss recent progress in
the theoretical study of several relativistic effects in laser-atom
interactions: influence of the magnetic component of the laser field,
relativistic mass shift due to the dressing of the electron mass by the laser
field, negative energy states and spin effects. Particular attention will be
paid to the modifications of the laser-atom dynamics in the high-intensity,
high-frequency regime where non-relativistic theories predict a decrease of
the ionization probability of atoms with increasing laser intensity.