<p>Astrophysical magnetic fields shape the dynamics of various astrophysical phenomena, from the formation of stars and galaxies to the acceleration of cosmic rays and the generation of powerful astrophysical jets. Intense laser-produced plasmas offer a unique laboratory environment for studying the fundamental properties of these magnetic fields and their interactions, under extreme conditions that are analogous to those astrophysical environments. This Review outlines the processes that govern the generation, amplification and transport of astrophysical magnetic fields and describes experiments using intense laser-produced plasmas that can test existing models and provide further insight.</p>