As black holes accrete surrounding gas, they often
produce relativistic, collimated outflows, or jets. Jets are expected to form
in the black hole vicinity making them powerful probes of strong-field gravity.
However, how jet properties are connected to black hole and accretion flow
properties has been unclear. Recent progress in computer simulations of black
hole accretion enables studies of jet formation in unprecedented detail. For
the first time, 3D general relativistic magnetohydrodynamic numerical
simulations allow one to determine the maximum efficiency with which accretion
onto black holes can power relativistic jets. I will present the dependence of
this maximum efficiency on black hole spin and discuss how this dependence
allows one to probe strong-field gravity. In realistic astrophysical systems,
the angular momentum vector of the accretion flow can be tilted relative to the
spin of the black hole. I will present the first simulations of jets from such
tilted accretion systems and discuss their observational signatures.