I will present grid-adaptive computational studies of both magnetized and unmagnetized jet flows, with significantly relativistic bulk speeds, as appropriate for AGN jets. Our relativistic jet studies shed light on the observationally established classification of Fanaroff-Riley galaxies, where the appearance in radio maps distinguishes two types of jet morphologies. We investigate how density changes in the external medium can induce one-sided jet decelerations, explaining the existence of hybrid morphology radio sources. Our simulations explore under which conditions highly energetic FR II jets may suddenly decelerate and continue with FR I characteristics. In a related investigation, we explore the role of dynamically important, organized magnetic fields in the collimation of the relativistic jet flows. In that study, we concentrate on morphological features of the bow shock and the jet beam, for various jet Lorentz factors and magnetic field helicities. We show that the helicity of the magnetic field is effectively transported down the beam, with compression zones in between diagonal internal cross-shocks showing stronger toroidal field regions. For the high speed jets considered, significant jet deceleration only occurs beyond distances exceeding hundred jet radii, as the axial flow can reaccelerate downstream to internal cross-shocks. This reacceleration is magnetically aided, due to field compression across the internal shocks which pinch the flow.