Magnetorotational instability (MRI) and Tayler instability (TI) are
reviewed in their meaning for the angular momentum transport in
protostellar disks and radiation zones of main-sequence stars.
The possible importance of the Hall effect for the stability of cool
disks, the structure and evolution of the magnetic solar tachocline
and new results for the TI-induced viscosity and chemical mixing in
radiative zones of hot stars (their Schmidt number) are special topics
of the discussion.
Also details about the successful realisation of the MRI in the
MHD-laboratory of the Forschungszentrum Dresden-Rossendorf ('PROMISE')
and the first setup for a coming TI-experiment (in Taylor-Couette geometry, without and with rotation) are presented.