The fundamental physics of high-field laser-matter interactions has driven ultrashort pulse generation to achieve record power densities of 10 22 Watts per cm 2 in focal spot sizes (FWHM) of 0.8 μm 1. These enormous fields are generated by compressing longer, high energy pulses to ever shorter lengths using so-called CPA compressors. Great care has to be taken to achieve such record power densities by controlling the spatio-temporal shape during pulse compression. Despite these remarkable experimental achievements, there have been relatively few developments on the theoretical side to derive realistic physical optical material models coupled to sophisticated E.M propagators. Many of the theoretical analysis tools developed in this emerging field of extreme nonlinear optics are restricted to oversimplified ID models that completely ignore the complex vector spatio-temporal couplings occurring within such small nonlinear interaction volumes. The advent of these high power ultra-short pulsed laser systems has opened up a whole new vista of applications and computational challenges. The applications space spans relatively short propagation lengths of centimeters to meters to a target up to many kilometers in atmospheric propagation studies. The high local field intensities generated within the pulse can potentially lead to electromagnetic carrier wave shocking so it becomes necessary to fully resolve the optical carrier wave within the 3D propagating pulse envelope. High local field intensities also lead to an explosive growth of the white-light supercontinuum spectrum and the intensities of even remote spectral components can be high enough to generate nonlinear coupling to the host material. For this reason, spectrally local models of light-matter coupling are expected to fail. In this paper, we will present a fully carrier-resolved E.M. propagator that allows for few meter long propagation lengths while fully resolving the optical carrier wave. Our applications focus will be on the relatively low intensity regime where critical self-focusing collapse in air or water can lead to very strong non-paraxial ultra-broadband excitations. One reason for this restriction is that we do not yet have computationally feasible robust physical models for ultra-broadband excitation of materials where nonlinear dispersion and absorption become dominant. The propagation of terawatt femtosecond duration pulses in the atmosphere can be qualitatively captured by physical models that include reliable linear dispersion/absorption while treating the nonlinear terms as spectrally local. We will review some recent experimental results by the German-Franco Teramobile team on atmospheric propagation, penetration through obscurants and remote laser induced breakdown spectroscopy. As a second application example will address the issue of strongly non-paraxial spectral superbroadening of femtosecond pulses while propagating in water - these latter nonlinear interactions generate so-called nonlinear X- and O-waves depending on the optical carrier wavelength of the initial pulse.