In astrophysical settings, differentially rotating systems are very common and magnetic fields are ubiquitous. In particular, thin disks of gas are often found around forming stars or in binary star systems, where they are known as accretion disks. Accretion disks are also commonly present in the centre of galaxies, and in some cases can be extremely luminous: quasars, for example, are thought to originate from a gaseous disk surrounding a very massive black hole. Our modern understanding of the MRI arose from attempts to understand the behavior of accretion disks in the presence of magnetic fields; it is now understood that the MRI is likely to occur in a very wide variety of different systems.