Long-lived, stable jets are observed in a wide variety of systems, from protostars, through Galactic compact objects to active galactic nuclei (AGN). Magnetic fields play a central role in launching, accelerating, and collimating the jets through various media. The termination of jets in molecular clouds or the interstellar medium deposits enormous amounts of mechanical energy and momentum, and their interactions with the external medium, as well, in many cases, as the radiation processes by which they are observed, are intimately connected with the magnetic fields they carry. This review focuses on the properties and structures of magnetic fields in long-lived jets, from their launch from rotating magnetized young stars, black holes, and their accretion discs, to termination and beyond. We compare the results of theory, numerical simulations, and observations of these diverse systems and address similarities and differences between relativistic and non-relativistic jets in protostellar versus AGN systems. On the observational side, we focus primarily on jets driven by AGN because of the strong observational constraints on their magnetic field properties, and we discuss the links between the physics of these jets on all scales.