"This project will be aimed at obtaining a deeper insight into the physical processes taking place in astrophysical magnetized plasmas. To study these scenarios I will employ different numerical codes as virtual tools that enable me to experiment on computers (virtual labs) with distinct initial and boundary conditions. Among the kind of sources I am interested to consider, I outline the following: Gamma-Ray Bursts (GRBs), extragalactic jets from Active Galactic Nuclei (AGN), magnetars and collapsing stellar cores. A number of important questions are still open regarding the fundamental properties of these astrophysical sources (e.g., collimation, acceleration mechanism, composition, high-energy emission, gravitational wave signature). Additionally, there are analytical issues on the formalism in relativistic dynamics not resolved yet, e.g., the covariant extension of resistive magnetohydrodynamics (MHD). All these problems are so complex that only a computational approach is feasible. I plan to study them by means of relativistic and Newtonian MHD numerical simulations. A principal focus of the project will be to assess the relevance of magnetic fields in the generation, collimation and ulterior propagation of relativistic jets from the GRB progenitors and from AGNs. More generally, I will pursue the goal of understanding the process of amplification of seed magnetic fields until they become dynamically relevant, e.g., using semi-global and local simulations of representative boxes of collapsed stellar cores. A big emphasis will be put on including all the relevant microphysics (e.g. neutrino physics), non-ideal effects (particularly, reconnection physics) and energy transport due to neutrinos and photons to account for the relevant processes in the former systems. A milestone of this project will be to end up with a numerical tool that enables us to deal with General Relativistic Radiation Magnetohydrodynamics problems in Astrophysics."