Theory of MHD waves in the solar corona

Considerable progress has recently been made in the exploration of oscillations in the corona. A variety of local wave phenomena have been detected in coronal loops and polar plumes (as well as in prominences and globally in the corona). Timescales ranging from seconds to tens of minutes have been found. Here we review the theoretical developments that have been used to interpret the properties of observed oscillations in coronal loops and plumes. Magnetohydrodynamic theory is found to give a good description of the waves. Both standing and impulsively excited waves axe invoked. The enigmatic rapid damping of the observed oscillations is discussed, with theoretical explanations in terms of resonant absorption, phase mixing or enhanced viscosity examined.Coronal oscillations provide an invaluable means of better understanding the corona, giving rise to the new field of coronal seismology.