Radio pulsars provide us with some of the most stable clocks in the universe. Nevertheless several pulsars exhibit sudden spin-up events, known as glitches. More than forty years after their first discovery, the exact origin of these phenomena is still open to debate. It is generally thought that they an observational manifestation of a superfluid component in the stellar interior and provide an insight into the dynamics of matter at extreme densities. In recent years there have been several advances on both the theoretical and observational side, that have provided significant steps forward in our understanding of neutron star interior dynamics and possible glitch mechanisms. In this article we review the main glitch models that have been proposed and discuss our understanding, in the light of current observations.Radio pulsars are thought to be rotating magnetised neutron stars (NS). The huge moment of inertia (of the order of 10 45 g cm 2 ) leads to exceptionally stable rotation rates and provides us with some of the most precise clocks in the universe. The best timed millisecond pulsars are stable to a precision which rivals that of atomic clocks [1]. Nevertheless radio pulsars exhibit several timing irregularities, the most striking of which are the so-called glitches. While most objects are observed to steadily spin-down due to the emission of electromagnetic and, possibly, gravitational waves, many pulsars show sudden increases in their spin, in some cases followed by an increase in their spin-down rate, i.e. glitches. Most pulsars also show slower, long-term, stochastic deviations from a regular spin-down law, that are generally classed as 'timing noise' and are not the main focus of this review article.Soon after the discovery of the first glitches in the Vela [2,3] and Crab [4,5] pulsars in 1969, several mechanisms were suggested to explain these phenomena. Although some initial suggestions featured external mechanisms, such as plasma explosions in the magnetosphere [6] or planets around the pulsar [7], the lack of radiative and pulse profile changes associated with these events was taken as evidence for an internal origin. The situation is different for rotating radio transients (RRATs) and magnetars, which are now known to glitch and do exhibit, amongst other peculiar traits, radiative changes associated with these events [8][9][10][11]. Magnetospheric activity is likely to play a role in these objects, as we discuss below.There are two main internal glitch mechanisms that have been examined in the literature. The first set of models relies on the fact that the outer layers of a neutron star form a crystalline crust that can support stress. As the NS spins down, the liquid core adjusts its shape to the rotation rate, while the solid crust maintains the shape appropriate for the previous, higher, spin rate. This leads to an increasing amount of strain building up in the crust, which is eventually released in the form of a star quake. The quake causes a sudden rearrangement of the moment of inertia and...