Type I X-ray bursts are thought to be caused by thermonuclear Ñashes in the surface layers of accreting neutron stars. Recent theoretical work has shown that, contrary to what was previously thought, strongly magnetic neutron stars can produce X-ray bursts. More recently, observations with the Rossi X-Ray T iming Explorer satellite have revealed that many X-ray bursts exhibit large-amplitude brightness oscillations. In this review, we summarize the observed features of X-ray bursts and the key elements of the thermonuclear Ñash model of this phenomenon. We then describe the recent theoretical and observational discoveries and discuss their implications for the nature and properties of X-ray bursts.