  Burst oscillations, a phenomenon observed in a significant fraction of Type I
(thermonuclear) X-ray bursts, involve the development of highly asymmetric
brightness patches in the burning surface layers of accreting neutron stars.
Intrinsically interesting as nuclear phenomena, they are also important as
probes of dense matter physics and the strong gravity, high magnetic field
environment of the neutron star surface. Burst oscillation frequency is also
used to measure stellar spin, and doubles the sample of rapidly rotating (above
10 Hz) accreting neutron stars with known spins. Although the mechanism remains
mysterious, burst oscillation models must take into account thermonuclear flame
spread, nuclear processes, rapid rotation, and the dynamical role of the
magnetic field. This review provides a comprehensive summary of the
observational properties of burst oscillations, an assessment of the status of
the theoretical models that are being developed to explain them, and an
overview of how they can be used to constrain neutron star properties such as
spin, mass and radius.
