  We discuss the relevance of the magnetorotational instability (MRI) in
core-collapse supernovae (CCSNe). Our recent numerical studies show that in
CCSNe, the MRI is terminated by parasitic instabilities of the Kelvin-Helmholtz
type. To determine whether the MRI can amplify initially weak magnetic fields
to dynamically relevant strengths in CCSNe, we performed three-dimensional
simulations of a region close to the surface of a differentially rotating
proto-neutron star in non-ideal magnetohydrodynamics with two different
numerical codes. We find that under the conditions prevailing in proto-neutron
stars, the MRI can amplify the magnetic field by (only) one order of magnitude.
This severely limits the role of MRI channel modes as an agent amplifying the
magnetic field in proto-neutron stars starting from small seed fields.
