Local hydromagnetic simulations of accretion-disc turbulence currently prov
ide the most convincing evidence that the origin of turbulence in discs cou
ld be the Balbus-Hawley magnetorotational instability. The main results of
such calculations are highlighted with particular emphasis on the generatio
n of large-scale magnetic fields. Comparison with mean-field dynamo theory
is made. This theory is then used to address the question of the launching
and collimation of winds emanating from the disc surfaces.