  Topological states nurtures the emergence of devices with unprecedented
functions in photonics, plasmonics, acoustics and phononics. As one of the
recently discovered members, higher-order topological insulators (HOTIs) have
been increasingly explored, featuring lower-dimensional topological boundary
states, leading to rich mechanisms for topological manipulation, guiding and
trapping of classical waves. Here, we provide an overview of current
developments of HOTIs in classical waves including basic principles, unique
physical properties, various experimental realizations, novel phenomena and
potential applications. Based on these discussions, we remark on the trends and
challenges in this field and the impacts of higher-order topology on other
research fields.
