  According to the general-relativistic no-hair theorem, astrophysical black
holes depend only on their masses and spins and are uniquely described by the
Kerr metric. Mass and spin are the first two multipole moments of the Kerr
spacetime and completely determine all other moments. The no-hair theorem can
be tested by measuring potential deviations from the Kerr metric which alter
such higher-order moments. In this review, I discuss tests of the no-hair
theorem with current and future observations of such black holes across the
electromagnetic spectrum, focusing on near-infrared observations of the
supermassive black hole at the Galactic center, pulsar-timing and very-long
baseline interferometric observations, as well as X-ray observations of
fluorescent iron lines, thermal continuum spectra, variability, and
polarization.
