The development of intense XUV sources through free-electron lasers (FELs) and high-order harmonic generation (HHG) in the femtosecond (fs) and sub-fs domains provides a unique tool to investigate non-linear ultrafast laser-matter interaction. In the study of the dynamics of molecular photoionization at ultrashort timescales, the Time-Dependent Schrödinger Equation (TDSE) has been crucial for the interpretation of experimental observations. In this thesis, we present results for ab initio calculations of H2 photoionization with UV/X-ray ultrashort laser pulses. We focus on the study of non-linear processes involving two photons and their role in the coupled electron-nuclear dynamics they induce and their study beyond the dipole approximation (DA). Our theoretical approach is based on a spectral method, which requires determining the quantum states of the field-free molecule. These states are calculated in the Born-Oppenheimer approximation employing a configuration interaction scheme together with multichannel scattering theory to determine for the treatment of continuum states, and the Feshbach partitioning formalism to account for autoionization. We resort to a multipolar expansion of the vector potential in the Coulomb gauge, from which we keep the terms corresponding to DA and retardation effects up to O(1/c), to account for the interaction with radiation. Finally, we make use of perturbative and non-perturbative propagation schemes to obtain transition amplitudes from which we can extract cross-sections, photoelectron spectra (PES), and molecular frame angular distributions (MFPADs).In the first part of the results, we demonstrate the coherent control of ionization and dissociation achieved by filtering the higher harmonics in an attosecond pulse train (APT) in an XUV pump-UV probe scheme. By solving the TDSE in DA including electronic and nuclear motion, we are able to extract nuclear and electronic kinetic energy release (KER) spectra to analyze the main ionization pathways as afunction of the delay between pump and probe. We then discuss the effect of harmonic filtering in manipulating one-photon against two-photon ionization yields, dissociative ionization channels, and asymmetries in the MFPADs. In the second part of the results of the thesis, we report the first calculations of Stimulated Raman Scattering (SRS) and Stimulated Compton Scattering (SCS) in H2 with intense X-ray laser fields. These non-linear phenomena consist in the absorption of a photon and the subsequent stimulated emission of a less energetic one leaving the molecule in an excited state (SRS) or effectively ionizing it (SCS). Theoretically, the inclusion of effects beyond DA becomes mandatory. We begin by investigating the relative role of the dipole (A.P) and non-dipole (A2) interaction terms through a perturbative study of the Raman cross-section. The role of the high energy electronic continuum in the partial cancellation of the dipole contribution is also analyzed. We then present results from SRS and SCS calculations using ultra-short pulses in which we compare the relative contribution of the dipole and non-dipole routes as a function of the photon energy. We assert the validity of perturbation theory by directly comparing SRS calculations with results obtained by solving the TDSE. In SCS, the interference between dipole and non-dipole routesproduces asymmetries in the MFPADs, which we analyze. Special attention is givento the effect of molecular orientation.Finally, we study SCS with two colors, focusing on the effect of the angle between the pulse propagation directions. As seen in atoms, non-dipole effects are enhanced for counter-propagating pulses. We also investigate the effect of color separation in energy.