  There is compelling evidence showing that extragalactic jets are a crucial
ingredient in the evolution of host galaxies and their environments.
Extragalactic jets are well collimated and relativistic, both in terms of
thermodynamics and kinematics at sub-parsec and parsec scales. They generate
strong shocks in the ambient medium, associated with observed hotspots in FRII
radio galaxies, and carve cavities that are filled with the shocked jet flow,
dragging a large fraction of the interstellar gas along, in the form of slow,
massive outflows within the host galaxies. In this paper, I discuss relevant
processes associated to jet evolution in the frame of FRI-FRII dichotomy. In
particular, I focus on the role of 1) the interaction between galactic
atmospheres and the jet head on global FRII jet kinematics, and 2) mass load by
stellar winds or small-scale instabilities on jet deceleration in FRI jets. The
results presented are based on 3D relativistic hydrodynamical (RHD) and/or 2D
axisymmetric, time-independent relativistic magnetohydrodynamical (RMHD)
simulations.
