Type-I X-ray bursts arise from unstable thermonuclear burning of accreted fuel on the surface of neutron stars. In this chapter we review the fundamental physics of the burning processes, and summarise the observational, numerical, and nuclear experimental progress over the preceding decade. We describe the current understanding of the conditions that lead to burst ignition, and the influence of the burst fuel on the observational characteristics. We provide an overview of the processes which shape the burst X-ray spectrum, including the observationally elusive discrete spectral features. We report on the studies of timing behaviour related to nuclear burning, including burst oscillations and mHz quasi-periodic oscillations. We describe the increasing role of nuclear experimental physics in the interpretation of astrophysical data and models. We survey the simulation projects that have taken place to date, and chart the increasing dialogue between modellers, observers, and nuclear experimentalists. Finally, we identify some open problems with prospects of a resolution within the timescale of the next such review.
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