  The role of outflows in the formation of stars and the protostellar disks
that generate them is a central question in astrophysics. Outflows are
associated with star formation across the entire stellar mass spectrum. In this
review, we describe the observational, theoretical, and computational advances
on magnetized outflows, and their role in the formation of disks and stars of
all masses in turbulent, magnetized clouds. The ability of torques exerted on
disks by magnetized winds to efficiently extract and transport disk angular
momentum was developed in early theoretical models and confirmed by a variety
of numerical simulations. The recent high resolution ALMA observations of disks
and outflows now confirm several key aspects of these ideas, e.g. that jets
rotate and originate from large regions of their underlying disks. New insights
on accretion disk physics show that magneto-rotational instability (MRI)
turbulence is strongly damped, leaving magnetized disk winds as the dominant
mechanism for transporting disk angular momentum. This has major consequences
for star formation, as well as planet formation. Outflows also play an
important role in feedback processes particularly in the birth of low mass
stars and cluster formation. Despite being almost certainly fundamental to
their production and focusing, magnetic fields in outflows in protostellar
systems, and even in the disks, are notoriously difficult to measure. Most
methods are indirect and lack precision, as for example, when using
optical/near-infrared line ratios. Moreover, in those rare cases where direct
measurements are possible - where synchrotron radiation is observed, one has to
be very careful in interpreting derived values. Here we also explore what is
known about magnetic fields from observations, and take a forward look to the
time when facilities such as SPIRou and the SKA are in routine operation.
