  Particle acceleration in relativistic jets to very high energies occurs at
the expense of the dissipation of magnetic or kinetic energy. Therefore,
understanding the processes that can trigger this dissipation is key to the
characterization of the energy budgets and particle acceleration mechanisms at
action in active galaxies. Instabilities and entrainment are two obvious
candidates to trigger dissipation. On the one hand, supersonic, relativistic
flows threaded by helical fields, as expected from the standard formation
models of jets in supermassive black-holes, are unstable to a series of
magnetohydrodynamical instabilities, such as the Kelvin-Helmholtz,
current-driven, or possibly the pressure-driven instabilities. Furthermore, in
the case of expanding jets, the Rayleigh-Taylor and centrifugal instabilities
may also develop. With all these destabilizing processes at action, a natural
question is how can some jets keep their collimated structure along hundreds of
kiloparsecs. On the other hand, the interaction of the jet with stars and
clouds of gas that cross the flow in their orbits around the galactic centers
provides another scenario in which kinetic energy can be efficiently converted
into internal energy and particles can be accelerated to non-thermal energies.
In this contribution, I review the conditions under which these processes occur
and their role both in jet evolution and propagation and energy dissipation.
