  High amplitude, nearly coherent X-ray brightness oscillations during
thermonuclear X-ray bursts were discovered with the Rossi X-ray Timing Explorer
(RXTE) in early 1996. Spectral and timing evidence strongly supports the
conclusion that these oscillations are caused by rotational modulation of the
burst emission and that they reveal the spin frequency of neutron stars in low
mass X-ray binaries, a long sought goal of X-ray astronomy. Studies carried out
over the past year have led to the discovery of burst oscillations in four new
sources, bringing to ten the number with confirmed burst oscillations. I review
the status of our knowledge of these oscillations and indicate how they can be
used to probe the physics of neutron stars. For a few burst oscillation sources
it has been proposed that the strongest and most ubiquitous frequency is
actually the first overtone of the spin frequency and hence that two nearly
antipodal hot spots are present on the neutron star. This inference has
important implications for both the physics of thermonuclear burning as well as
the mass - radius relation for neutron stars, so its confirmation is crucial. I
discuss recent attempts to confirm this hypothesis for 4U 1636-53, the source
for which a signal at the putative fundamental (290 Hz) has been claimed.
