Published online by Cambridge University Press: 04 August 2017
The last ten years of observations have shown beyond doubt the fundamental role played by the magnetic field in the heating of stellar atmospheres. After the recognition of the extreme inhomogeneity of the solar corona, two basic new trends have appeared in the theoretical literature on the coronal heating problem. One is the adoption of a global point of view that stresses the connection of the properties of the upper layers to those of the underlying ones. In this way a general framework is provided, capable of accomodating many possible heating mechanisms that need not to be specified at this stage. The second novelty is the explicit inclusion in the theory of the inhomogeneous nature of the stellar envelopes, as a result of the presence of magnetic fields. The present status of knowledge on the subject as determined by the above evolution of the theoretical approach will be reviewed.