One of the great problems of astrophysics is the unanswered question about the origin and mechanism of chromospheric and coronal heating. Just how these outer stellar envelopes are heated is of fundamental importance, since all stars have hot chromospheric and coronal shells where the temperature rises to millions of degrees, comparable to the temperatures in the stars' cores. Here for the first time is a comprehensive inventory of the proposed chromospheric and coronal heating theories. The proposed heating processes are critically compared, and the observational evidence for the various...