  Kink oscillations of coronal loops, i.e., standing kink waves, is one of the
most studied dynamic phenomena in the solar corona. The oscillations are
excited by impulsive energy releases, such as low coronal eruptions. Typical
periods of the oscillations are from a few to several minutes, and are found to
increase linearly with the increase in the major radius of the oscillating
loops. It clearly demonstrates that kink oscillations are natural modes of the
loops, and can be described as standing fast magnetoacoustic waves with the
wavelength determined by the length of the loop. Kink oscillations are observed
in two different regimes. In the rapidly decaying regime, the apparent
displacement amplitude reaches several minor radii of the loop. The damping
time which is about several oscillation periods decreases with the increase in
the oscillation amplitude, suggesting a nonlinear nature of the damping. In the
decayless regime, the amplitudes are smaller than a minor radius, and the
driver is still debated. The review summarises major findings obtained during
the last decade, and covers both observational and theoretical results.
Observational results include creation and analysis of comprehensive catalogues
of the oscillation events, and detection of kink oscillations with imaging and
spectral instruments in the EUV and microwave bands. Theoretical results
include various approaches to modelling in terms of the magnetohydrodynamic
wave theory. Properties of kink oscillations are found to depend on parameters
of the oscillating loop, such as the magnetic twist, stratification, steady
flows, temperature variations and so on, which make kink oscillations a natural
probe of these parameters by the method of magnetohydrodynamic seismology.
