  In the present review article, we discuss the recent developments in studying
the Kelvin--Helmholtz (KH) instability of magnetohydrodynamic (MHD) waves
propagating in various solar magnetic structures. The main description is on
the modeling of KH instability developing in the coronal mass ejections (CMEs),
and contributes to the triggering of wave turbulence subsequently leading to
the coronal heating. KH instability of MHD waves in coronal active regions
recently observed and imaged in unprecedented detail in EUV high cadence,
high-resolution observations by SDO/AIA, and spectroscopic observations by
Hinode/EIS instrument, is posing now challenge for its realistic modeling. It
is shown that considering the solar mass flows of CMEs as moving cylindrical
twisted magnetic flux tubes, the observed instability can be explained in terms
of unstable m = -3 MHD mode. We also describe the occurrence of the KH
instability in solar jets. The obtained critical jet speeds for the instability
onset as well as the linear wave growth rates are in good agreement with the
observational data of solar jets.
