MHD wave theory predicts at least three distinct eigensolutions in a uniform and magnetised plasmas. However, apace (Hinode, SDO, IRIS) and ground-based (DST/ROSA, IBIS, CoMP, STT/CRISP) observations have provided plenty of compelling evidence of waves present in the highly non-uniform and structured solar atmosphere. The detection and analysis of waves these waves are challenges on their own. Identification is very hard, often debated.
First, I'll summarise the recent advances in MHD wave theory providing a wide range of visualisation that help us in the wave identification. In particular, I'll discuss the so-called sausage and kink magneto-acoustic waves, and the much sought-after Alfven waves. An accurate understanding of these waves allows us to perform sub-resolution solar magneto-seismology (SMS). Next, I will concentrate on the role of the various MHD waves, and will discuss the latest status on detecting them in a range of solar waveguides (sunspots, pores, magnetic bright points, coronal loops).
Within the framework of MHD I will discuss their origin and generation mechanism of these waves. Finally, I will embark on showing how MHD waves help us to diagnose the solar plasma and may bring us closer to solving the century-old solar atmospheric heating enigma.