  In the past few years observations by high-resolution space imaging
telescopes and spectrometers have confirmed that a great variety of MHD waves
are supported in the solar corona of a low-beta plasma and fine structure. MHD
waves are an important diagnostic tool for the determination of the physical
parameters of coronal loops, dubbed {\em coronal seismology}. In this paper, I
will review recent results of both propagating and standing waves observed with
SOHO and TRACE, and discuss the wave damping and excitation mechanisms as well
as some applications of coronal seismology based on recent numerical
simulations and theories in relation to the observations.
