We will present the “MaReLAP” (Magnetized Relativistic Laboratory Astrophysics Plasmas) megagrant project, which aims at tackling, in the laboratory, some of the most basic questions, yet unresolved, about the physical mechanisms leading to observed astrophysical phenomena. Our approach is to produce laboratory plasmas that are scalable to astrophysical objects, using a unique combination of magnetic fields, intense microwaves and laser sources. Using such “laboratory astrophysics” approach, at the intersection of astrophysics, laser physics and plasma physics, we will perform a number of studies of processes in plasmas of various nature. This includes shock waves and plasma emission (jets) in the vicinity of young or evolved stars, or hot non-equilibrium plasma circulating in magnetic loops or bursting from of them in order e.g. to model plasma parameters typical for the Sun, other stars and accretion disks around compact objects.