Rapid progress in recent years in the development of high power ultra-short pulse laser systems has opened up a whole new vista of applications and computational challenges. New experimental developments in the field of extreme nonlinear optics will require more rigorous electromagnetic propagation models beyond those existing in the current literature. In this chapter, we derive a 3D time domain unidirectional vector Maxwell propagator that resolves the underlying optical carrier wave while allowing propagation over macroscopic many-meter distances. Our model allows for extreme focusing conditions down to the order of the wavelength in the material. A novel aspect of our approach is that the pulse propagator is designed to faithfully capture the light-material interaction over the broad spectral landscape of relevance to the interaction. Moreover the model provides a seamless and physically self-consistent means of deriving the many ultra-short pulse propagation equations presented in the literature. Amongst current applications that are most challenging from a computational point of view are those involving critical self-focusing with concomitant explosive growth in the generated light spectrum. Specific application areas chosen for illustration include multiple filament formation during propagation of ultra-intense femtosecond laser pulses in air and nonlinear self-trapping in condensed media. These examples exhibit rather different aspects of intense femtosecond pulse propagation and demonstrate the robustness and flexibility of our recently formulated unidirectional Maxwell propagator. A clear message to emerge from our study is the inadequacy of spectrally local light-material interaction models when nonlinear coupling exists over many hundreds of nanometer frequency bandwidths. More sophisticated, computationally feasible, models of nonlinear dispersion are needed.