  While the spectrum of non-strange light mesons is well known, many predicted
strange mesons have not yet been observed, and many potentially observed states
require further confirmation. Using the $K^-$ component of the hadron beam at
the M2 beamline at CERN, we study the strange-meson spectrum with the COMPASS
experiment. The flagship channel is the $K^-\pi^-\pi^+$ final state, for which
COMPASS has obtained the world's largest sample. Based on this sample, we have
performed the most detailed and comprehensive partial-wave analysis of this
final state to date. For example, we observe a clear signal from the well-known
$K_2^*(1430)$, and for the first time we study the $K_2(1770)$, $K_2(1820)$,
and $K_2(2250)$ in a single analysis. We also find evidence for a supernumerary
signal called $K(1630)$, suggesting that this signal is a pseudoscalar exotic
strange meson.
