I will present MHD simulations investigating the launching of astrophysical jets. First, a brief introduction into MHD wind and jets is given. Our simulations treat the time-dependent evolution of the accretion-ejection structure and the subsequent collimation of the disk wind into a high-velocity jet. The setup considers various models for a physical (turbulent) magnetic diffusivity that is essential for the mass loading of the outflow. We find relatively high mass fluxes in the outflow, about 20-40% of the accretion rate. Recent simulations include a mean-field accretion disk dynamo and the launching of outflows by a self-generated disk magnetic field. We have run a parameter survey of disk-wind launched by disk of different magnetization and find that the disk magnetization is the main parameter that governs the jet dynamics. Special relativistic jet formation simulations allow to construct synchrotron radiation maps from the dynamical outflow structure that can be compared to the observations. Finally I will present preliminary results from GR-MHD simulations treating the accretion-ejection structure of outflows from resistive accretion disks.