  I review our understanding of the thermonuclear instabilities on accreting
neutron stars that produce Type I X-Ray bursts. I emphasize those observational
and theoretical aspects that should interest the broad audience of this
meeting. The easily accessible timescales of the bursts (durations of tens of
seconds and recurrence times of hours to days) allow for a very stringent
comparison to theory. The largest discrepancy (which was found with EXOSAT
observations) is the accretion rate dependence of the Type I burst properties.
Bursts become less frequent and energetic as the global accretion rate
increases, just the opposite of what the spherical theory predicts. I present a
resolution of this issue by taking seriously the observed dependence of the
burning area on the global accretion rate, which implies that as the accretion
rate increases, the accretion rate per unit area decreases. This resurrects the
unsolved problem of knowing where the freshly accreted material accumulates on
the star, equally relevant to the likely signs of rotation during the bursts
summarized by Swank at this meeting. I close by highlighting the Type I bursts
from GS 1826-238 that were found with BeppoSAX and RXTE. Their energetics,
recurrence times and temporal profiles clearly indicate that hydrogen is being
burned during these bursts, most likely by the rapid-proton (rp) process.
