Magnetic waves are a relevant component in the dynamics of the solar
atmosphere. Their significance has increased because of their potential as a
remote diagnostic tool and their presumed contribution to plasma heating
processes. We discuss our current understanding on coronal heating by magnetic
waves, based on recent observational evidence and theoretical advances. The
discussion starts with a selection of observational discoveries that have
brought magnetic waves to the forefront of the coronal heating discussion.
Then, our theoretical understanding on the nature and properties of the
observed waves and the physical processes that have been proposed to explain
observations are described. Particular attention is given to the sequence of
processes that link observed wave characteristics with concealed energy
transport, dissipation, and heat conversion. We conclude with a commentary on
how the combination of theory and observations should help us understanding and
quantifying magnetic wave heating of the solar atmosphere.Comment: Accepted for publication in Royal Society of London Philosophical
Transactions Series