The magnetic field in the solar atmosphere is not uniformly distributed but
organized in typical configurations: e.g., intense flux tubes in the photo
sphere, magnetic loops in the corona, plumes in the solar wind. Each of the
se magnetic configurations can support magnetohydrodynamic (MHD) waves and
observations show that this is indeed the case. The intrinsic inhomogeneity
of the magnetic configurations enables local (slow and) Alfven waves to ex
ist on individual magnetic surfaces. These local Alfven waves provide a mea
ns for dissipating wave energy which is far more efficient in a weakly diss
ipative plasma than classical resistive or viscous MHD wave damping in a un
iform plasma. This property has inspired a lot of work on the dissipation o
f driven Alfven waves and wave heating in the solar atmosphere by resonant
absorption and phase mixing. This review concentrates on the interaction be
tween fast magnetosonic waves, local Alfven waves and quasimodes and discus
ses recent results on the time evolution of phase mixing of resonant waves
driven by footpoint motions. (C) 2001 American Institute of Physics.