  I review our theoretical understanding of thermonuclear flashes on accreting
neutron stars, concentrating on comparisons to observations. Sequences of
regular Type I X-ray bursts from GS 1826-24 and 4U 1820-30 are very well
described by the theory. I discuss recent work which attempts to use the
observed burst properties in these sources to constrain the composition of the
accreted material. For GS 1826-24, variations in the burst energetics with
accretion rate indicate that the accreted material has solar metallicity; for
4U 1820-30, future observations should constrain the hydrogen fraction, testing
evolutionary models. I briefly discuss the global bursting behavior of burst
sources, which continues to be a major puzzle. Finally, I turn to superbursts,
which naturally fit into the picture as unstable carbon ignition in a thick
layer of heavy elements. I present new time-dependent models of the cooling
tails of superbursts, and discuss the various interactions between superbursts
and normal Type I bursts, and what can be learned from them.
