I will present recent results of MHD simulations investigating the launching of astrophysical jets, covering both relativistic and non-relativistic flows. I will cover the topics of the
1) physical conditions at the launching point of jets,
2) the origin of the jet launching magnetic field as generated by a mean-field accretion disk dynamo, and
3) general relativistic jet launching from close to a black hole. I will start 0) with an introduction on the basic physics involved.