I review our theoretical understanding of thermonuclear flashes on accreting neutron stars, and how well the theory confronts observations of Type I X-ray bursts. While the global behavior of Type I bursting is not well-explained, I argue that the theory is successful in the regime of regular bursting, allowing us to learn about the accretion rate onto the star and composition of the accreted matter. To illustrate this, I describe recent work on the bursters GS 1826-238 and 4U 1820-30. I then discuss the spectacular "superbursts" discovered by long term monitoring programs in recent years. These very energetic bursts (1000 times the energy and duration of normal Type I bursts) fit naturally into the theoretical picture as unstable ignition of carbon in the ashes of normal Type I bursts. I emphasise that simultaneous modelling of normal Type I bursts and superbursts gives a powerful probe of the neutron star's outer layers. Finally, I discuss what we can learn about the dynamics of the burning from Type I burst oscillations, in particular emphasising the potential to probe the magnetic field of these neutron stars.