Relativistic extragalactic jets are formed in the vicinity of supermassive black-holes in active galactic nuclei (AGN), and they propagate through and out of the host galaxy along tens and hundreds of kiloparsecs. These jets are among the most powerful astrophysical scenarios known, involving time-integrated energies of the order of 1.e60 erg and powers ranging from 1.e42 to 1.e47 erg/s. On the one hand, their supersonic flows trigger strong shocks that propagate through the interstellar medium of their host galaxies and eventually through the intracluster medium and, on the other hand, they are subject to the development of instabilities and to deceleration by entrainment. In my talk, I will show that jet evolution is not only affected by its own properties, but also by those of the host galaxy, namely gas distribution and stellar population. I will also review several results that provide evidence for the host galaxy evolution being conditioned by the jet passage.