  Angular momentum transport in accretion disk has been the focus of intense
research in theoretical astrophysics for many decades. In the past twenty
years, MHD turbulence driven by the magnetorotational instability has emerged
as an efficient mechanism to achieve that goal. Yet, many questions and
uncertainties remain, among which the saturation level of the turbulence. The
consequences of the magnetorotational instability for planet formation models
are still being investigated. This lecture, given in September 2012 at the
school "Role and mechanisms of angular momentum transport in the formation and
early evolution of stars" in Aussois (France), aims at introducing the
historical developments, current status and outstanding questions related to
the magnetorotational instability that are currently at the forefront of
academic research.
