The propagation of femtosecond, multiterawatt, relativistic laser pulses in a transparent plasma is studied. The spatio-temporal dynamics of ultrashort, high-power laser pulses in underdense plasmas differs dramatically from that of long laser beams. We present the results of numerical studies of these dynamics within a model which systematically incorporates finite pulse length effects (i.e., dispersion) along with diffraction and nonlinear refraction in a strongly nonlinear, relativistic regime. New space-time patterns of self-compression, self-focusing and self-phase-modulation, typical of ultrashort, high-intensity laser pulses, are analyzed. The parameters of our numerical simulations correspond to a new class of high-peak-power (> 100 TW), ultrashort-pulsed laser systems, producing pulses with a duration in the 10 - 20 femtosecond range. Spatiotemporal dynamics of these self-effects and underlying physical mechanisms are discussed.