Many distinct classes of high-energy variability have been observed in astrophysical sources, on a range of timescales. The widest range (spanning microseconds-decades) is found in accreting, stellar-mass compact objects, including neutron stars and black holes. Neutron stars are of particular observational interest, as they exhibit surface effects giving rise to phenomena (thermonuclear bursts and pulsations) not seen in black holes. Here we briefly review the present understanding of thermonuclear (type-I) X-ray bursts. These events are powered by an extensive chain of nuclear reactions, which are in many cases unique to these environments. Thermonuclear bursts have been exploited over the last few years as an avenue to measure the neutron star mass and radius, although the contribution of systematic errors to these measurements remains contentious. We describe recent efforts to better match burst models to observations, with a view to resolving some of the astrophysical uncertainties related to these events. These efforts have good prospects for providing complementary information to nuclear experiments.
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