  Astrophysical jets are widely believed to be self-collimated by the
hoop-stress due to the azimuthal component of their magnetic field. However
this implies that the magnetic field is largely dominated by its azimuthal
component in the outer jet region. In the fusion context, it is well-known that
such configurations are highly unstable in static columns, leading to plasma
disruption. It has long been pointed out that a similar outcome may follow for
MHD jets, and the reasons preventing disruption are still not elucidated,
although some progress has been accomplished in the recent years.
  In these notes, I review the present status of this open problem for
pressure-driven instabilities, one of the two major sources of ideal MHD
instability in static columns (the other one being current-driven
instabilities).
  I first discuss in a heuristic way the origin of these instabilities.
Magnetic resonances and magnetic shear are introduced, and their role in
pressure-driven instabilities discussed in relation to Suydam's criterion. A
dispersion relation is derived for pressure-driven modes in the limit of large
azimuthal magnetic fields, which gives back the two criteria derived by
Kadomtsev for this instability. The growth rates of these instabilities are
expected to be short in comparison with the jet propagation time.
  What is known about the potential stabilizing role of the axial velocity of
jets is then reviewed. In particular, a nonlinear stabilization mechanism
recently identified in the fusion literature is discussed.
  Key words: Ideal MHD: stability, pressure-driven modes; Jets: stability
