Relativistic hydro and magnetohydrodynamics (MHD) provide a continuum fluid description for plasma dynamics characterized by shock-dominated flows approaching the speed of light. Significant progress in its numerical modelling emerged in the last two decades; we highlight selected examples of modern grid-adaptive, massively parallel simulations realized by our open-source software MPI-AMRVAC (Keppens et al 2012 J. Comput. Phys.231 718). Hydrodynamical models quantify how energy transfer from active galactic nuclei (AGN) jets to their surrounding interstellar/intergalactic medium (ISM/IGM) gets mediated through shocks and various fluid instability mechanisms (Monceau-Baroux et al 2012 Astron. Astrophys.545 A62). With jet parameters representative for Fanaroff–Riley type-II jets with finite opening angles, we can quantify the ISM volumes affected by jet injection and distinguish the roles of mixing versus shock-heating in cocoon regions. This provides insight in energy feedback by AGN jets, usually incorporated parametrically in cosmological evolution scenarios. We discuss recent axisymmetric studies up to full 3D simulations for precessing relativistic jets, where synthetic radio maps can confront observations. While relativistic hydrodynamic models allow one to better constrain dynamical parameters like the Lorentz factor and density contrast between jets and their surroundings, the role of magnetic fields in AGN jet dynamics and propagation characteristics needs full relativistic MHD treatments. Then, we can demonstrate the collimating properties of an overal helical magnetic field backbone and study differences between poloidal versus toroidal field dominated scenarios (Keppens et al 2008 Astron. Astrophys.486 663). Full 3D simulations allow one to consider the fate of non-axisymmetric perturbations on relativistic jet propagation from rotating magnetospheres (Porth 2013 Mon. Not. R. Astron. Soc.429 2482). Self-stabilization mechanisms related to the detailed magnetic pitch variations are discussed.