R. Erdelyi, University of Sheffield, robertus@sheffield.ac.uk

High spatial, temporal and spectral resolution satellite and ground-based observations have provided
plenty of evidence of periodic perturbations present in localised magnetised structures of the solar
atmosphere. Our understanding of these structures has changed considerably in light of these
observations. Identifying confidently MHD waves not only enable us to perform sub-resolution solar
magneto-seismology (SMS) but waves are also potential candidates to carry and damp the necessary
non-thermal energy in these localised waveguides. First, we will briefly outline the basic recent
developments in MHD wave theory focussing on linear waves.

Next, we will concentrate on the role of the most frequently studied wave classes, including the Alfven,
and magneto-acoustic kink and sausage waves. The current theoretical (and often difficult)
interpretations of the detected wave and oscillatory phenomena within the framework of MHD will be
addressed. The photospheric origin, the wave structures and how these waves penetrate into the
chromosphere, transition region or even into the corona will be discussed.

The latest reported observational findings of potential MHD wave flux, in terms of localised plasma
heating, with some surprising results will be discussed, bringing us closer to solve the solar
atmospheric heating problem.