Ground-based (e.g. DST/ROSA, IBIS, CoMP, STT/CRISP) and space-borne (e.g. SOHO, TRACE, STEREO, Hinode, SDO, IRIS, SPS) observations have discovered a wide range of waves and oscillations with a wealth of spatial and temporal scales of the magnetised solar atmosphere. Our understanding about localised solar structures has therefore been changed considerably in light of these fantastic discoveries. On the theory side, a popular interpretation of these periodic perturbations is within the framework of magneto-hydrodynamics. Thanks to MHD waves we are not only enable to perform sub-resolution solar magneto-seismology (SMS) but have also found them as potential candidates to carry and damp the observed non-thermal energy in localised MHD waveguides. 

First, we will briefly outline the basic recent developments in MHD wave theory focussing on linear MHD waves. We will introduce the concept of asymmetric MHD waveguide that may be an important aspect for the fantastic kitty: DKIST.

Next, we will concentrate on the role of the most frequently studied wave classes, including the mysterious Alfven, and magneto-acoustic sub-classes of kink and sausage waves. Finally, we will address how solar MHD waves, swirls and solar jet formation may all be related. We will argue to unite MHD wave and jet theories and demonstrate to develop a common modelling platform with solar applications. An example will be shown where prevalent swirls, in the form of Alfven pulses, propagate upwards through the solar atmosphere dragging with them jets and reach the chromospheric layers. We show why this maybe seen as an important step towards understanding better the heating enigma of the solar atmosphere.