My research concerns, broadly speaking, the modeling of high-energy density plasmas, created either in laboratory experiments using powerful lasers or during violent astrophysical events. In the former setting, I am particularly interested in the dynamics of plasmas driven by ultraintense (I > 10^18 W/cm^2), ultrashort (~0.01- 1 ps) laser pulses, leading to the acceleration of some, or all, of the target electrons to relativistic energies. The resulting extreme charge and current densities entail a wealth of phenomena (plasma instabilities, ion beam acceleration, energetic photon emissions, ultrafast plasma heating, shock waves, nuclear reactions, etc.) of fundamental or applied significance. Most of these being intertwined, their complete quantitative description necessitates first-principles, kinetic numerical simulations treating electromagnetic interactions of the plasma particles in a self-consistent manner. The development and exploitation of the particle-in-cell CALDER code, one of the reference tools in this field, is an important part of my work. Moreover, the similarity between some of the basic processes governing relativistic laser-plasma interactions (or beam-plasma interactions using conventional particle accelerators) and those underpinning a number of astrophysical scenarios led me to closely collaborate with astrophysicists, notably to study the microphysics of instability-mediated shock waves, widely believed to account for the generation of the most energetic particle and radiation sources in the Universe.