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.