In the context of magnetic confinement fusion, the basic magnetic field configuration consists of toroidally nested flux surfaces, while each flux surface is characterised by a certain value of the rotational transform or safety factor q. Magnetic islands can appear at flux surfaces with a rational value of the safety factor q = m/n.  Subsidiary islands can appear within an island.
The rupture of the assumed initial topology of toroidally nested flux surfaces needed to produce the island requires the reconnection of magnetic field lines, which can only occur with finite resistivity.  Stellarators may have a vacuum magnetic field structure that already contains some islands (so-called 'natural islands'). Since these are completely determined by the external magnetic field, they are static.
Island growth and saturation
The prediction of the non-linear saturated state of islands is the goal of Neoclassical Tearing Mode (NTM) theory. This theory has been developed to a considerable level of sophistication, although discrepancies with experimental observations remain. 
Islands can rotate within and/or with respect to the ambient plasma. The observation of such rotating 'MHD modes' is ubiquitous in fusion plasmas with typical frequencies of the order of several tens of kHz. The detection of such modes is possible by measuring perturbations of the magnetic field, or the electron density, temperature, or pressure. If the ambient magnetic field (produced by external coils) has an appropriate structure, the island can also lock onto that structure.  Locked islands often lead to a disruption (complete loss of confinement) in tokamaks.
It is generally assumed that the temperature is rapidly equilibrated along the magnetic field lines inside the island, so that radial transport is effectively short-circuited across the islands, decreasing the effective size of the main plasma.  However, it is possible to qualify this statement somewhat by taking into account the ratio between parallel and perpendicular transport within an island. 
Island control is possible by tailoring the q-profile, external magnetic fields,  and the pressure profile, or by spinning up the plasma.  Pressure effects can lead to 'island healing'.  Active control of islands by external means - in particular, Electron Cyclotron Heating and Current Drive - is also possible.   
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