Forthcoming multi-petawatt laser systems, such as the French Apollon and European Extreme Light Infrastructure facilities, are expected to deliver on-target laser intensities exceeding 10^22 W/cm^2. A novel regime of laser-matter interaction will ensue, where ultra-relativistic plasma effects are coupled with copious generation of high-energy photons and electron-positron pairs. This will pave the way for many transdisciplinary applications in fundamental and applied research, including the development of unprecedentedly intense, compact particle and radiation sources, the experimental investigation of relativistic astrophysical scenarios and tests of quantum electrodynamics theory.In recent years, most theoretical studies performed in this research field have focused on the impact of synchrotron photon emission and Breit-Wheeler pair generation, both directly induced by the laser field and believed to be dominant at intensities >10^22 W/cm^2. At the lower intensities (≲10^21 Wcm^(-2)) currently attainable, by contrast, photon and pair production mainly originate from, respectively, Bremsstrahlung and Bethe-Heitler/Trident processes, all triggered by atomic Coulomb fields. The conditions for a transition between these two regimes have, as yet, hardly been investigated, particularly by means of integrated kinetic numerical simulations. The purpose of this PhD is precisely to study the aforementioned processes under various physical scenarios involving extreme laser-plasma interactions. This work is carried out using the particle-in-cell CALDER code developed at CEA/DAM which, over the past few years, had been enriched with modules describing the synchrotron and Breit-Wheeler processes.Our first study aimed at extending the simulation capabilities of CALDER to the whole range of photon and positron generation mechanisms arising during relativistic laser-plasma interactions. To this purpose, we have implemented modules for the Coulomb-field-mediated Bremsstrahlung, Bethe-Heitler and Trident processes. Refined Bremsstrahlung and Bethe-Heitler cross sections have been obtained which account for electronic shielding effects in arbitrarily ionized plasmas. Following validation tests of the Monte Carlo numerical method, we have examined the competition between Bremsstrahlung/Bethe-Heitler and Trident pair generations by relativistic electrons propagating through micrometer copper foils. Our self-consistent simulations qualitatively agree with a 0-D theoretical model, yet they show that the deceleration of the fast electrons due to target expansion significantly impacts pair production.We then address the competition between Bremsstrahlung and synchrotron emission from copper foils irradiated at 10^22 Wcm^(-2). We show that the maximum radiation yield (into >10 keV photons) is achieved through synchrotron emission in relativistically transparent targets of a few 10 nm thick. The efficiency of Bremsstrahlung increases with the target thickness, and takes over synchrotron for >2μm thicknesses. The spectral properties of the two radiation processes are analyzed in detail and correlated with the ultrafast target dynamics.Finally, we investigate the potential of nanowire-array targets to enhance the synchrotron yield of a 10^22 Wcm^(-2) femtosecond laser pulse. Several radiation mechanisms are identified depending on the target parameters and as a function of time. A simulation scan allows us to identify the optimal target geometry in terms of nanowire width and interspacing, yielding a ∼10% radiation efficiency. In this configuration, the laser-driven nanowire array rapidly expands to form a quasi-uniform, relativistically transparent plasma. Furthermore, we demonstrate that uniform sub-solid targets can achieve synchrotron yields as high as in nanowire arrays, but that the latter enable a strong emission level to be sustained over a broader range of average plasma density.