Mem. S.A.It. Vol. 79, 1148 c  SAIt 2008 Memorie della N. Vlahakis Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, GR-15784 Zografos, Athens, Greece; e-mail: vlahakis@phys.uoa.gr Abstract. The main driving mechanism of relativistic jets is likely related to magnetic fields. These fields are able to tap the rotational energy of the central compact object or disk, accelerate and collimate matter ejecta. To zeroth order these outflows can be described by the theory of steady, axisymmetric, ideal magnetohydrodynamics. Results from recent numerical simulations of magnetized jets, as well as analytical studies, show that the effi- ciency of the bulk acceleration could be more than ∼ 50%. They also shed light to the degree of the collimation and how it is related to the pressure distribution of the environment, the apparent kinematics of jet components, and the observed polarization properties. Key words. MHD – relativity 1. Introduction The observed superluminal motion of the com- ponents of many AGN jets is a clear indica- tion of their relativistic motion. Unfortunately the apparent speed alone is not enough to give the true velocity of these outflows. It can only give a lower limit of the Lorentz factor γ =  1 − β 2  −1/2 , through the relation β app = β sin θ n (1 − β cos θ n ) −1 which also involves the angle θ n between the flow direction and the line of sight. In cases where the Doppler fac- tor δ ≡ γ −1 (1 − β cos θ n ) −1 can be also found, the two relations give the flow speed as a func- tion of distance from the core. For example Unwin et al. (1997), by combining radio and X-ray flux measurements and interpreting the latter as synchrotron self-Compton, deduced a change in the bulk Lorentz factor of the C7 component in 3C345, from γ ∼ 5 to γ ∼ 10 over a deprojected distance range of ∼ 3 − 20pc (they also infer a decrease in the Doppler fac- tor from 12 to 4 and an increase in the angle between the velocity of the component and the line of sight from 2 to 10 ◦ during the same period). Similarly Piner et al. (2003) inferred an acceleration from γ = 8 at r < 5.8pc to γ = 13 at r ≈ 17.4pc in 3C 279. Another way to estimate the Doppler factor is by comparing the variability timescale with the light-travel time across the emitting region (Jorstad et al., 2005). The extended (parsec scale) bulk acceler- ation seems to be a general characteristic of AGN jets. Besides the two examples men- tioned above, where an increase of the Lorentz factor was directly deduced, there are cases where there are observations of several su- perluminal features with the innermost one typically exhibiting the smallest proper mo- tion (e.g., Homan et al., 2001). Sikora et al. (2005) give a more general argument related to the extended acceleration: If the bulk flow near the disk is sufficiently fast (γ  5) it would Comptonize photons coming from the disk, producing bulk-Compton features. The