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We present results of magnetohydrodynamic (MHD) simulations of jet formation and propagation, discussing a variety of astrophysical setups. In the first approach we con-sider simulations of relativistic MHD jet formation, considering jets launched from the surface of a Keplerian disk, demonstrating numerically- for the first time- the self-collimating ability of relativistic MHD jets. We obtain Lorentz factors up to ' 10 while acquiring a high degree of collimation of about 1 degree. We then present synchrotron maps calculated from the intrinsic jet structure derived from the MHD jet formation sim-ulation. We finally present (non-relativistic) MHD simulations of jet lauching, treating the transition between accretion and ejection. These setups include a physical magnetic diffusivity which is essential for loading the accretion material onto the outflow. We find relatively high mass fluxes in the outflow, of the order of 20-40 % of the accretion rate. PACS numbers: 98.62.Mw, 95.30.Qd, 98.62.Nx, 98.38.Fs, 98.58.Fd 1