In a plasma interacting with ultra-short, high-intensity laser pulses,
the magnetic part of the Lorentz force on the electrons can become as
important as the electric part. In this case, we can expect the magne
tic field to change the pattern of the nonlinear laser-pulse-plasma in
teraction drastically. The relativistic nonlinearities introduced by t
he magnetic interaction are of general interest in relation to the fie
ld of ultra-strong electromagnetic waves propagating in media, high-en
ergy space plasmas and laser-plasma interaction under laboratory condi
tions. We present a summary of analytical and numerical results concer
ning the generation of quasi-static magnetic fields by high-intensity
laser pulses in underdense plasmas and in thin plasma foils, and discu
ss the dynamical effects of these fields on the plasma motion and on t
he pulse propagation. This analysis indicates that phenomena such as c
urrent pinching, reconnection of magnetic-field lines and vortex propa
gation etc, that have been previously discussed in the case of space a
nd laboratory plasmas, are also important for laser-plasma interaction
s.