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Tidal disruption events (TDEs) are among the brightest transients in theoptical, ultraviolet, and X-ray sky. These flares are set into motion when astar is torn apart by the tidal field of a massive black hole, triggering achain of events which is -- so far -- incompletely understood. However, thedisruption process has been studied extensively for almost half a century, andunlike the later stages of a TDE, our understanding of the disruption itself isreasonably well converged. In this Chapter, we review both analytical andnumerical models for stellar tidal disruption. Starting with relatively simple,order-of-magnitude physics, we review models of increasing sophistication, thesemi-analytic ``affine formalism,'' hydrodynamic simulations of the disruptionof polytropic stars, and the most recent hydrodynamic results concerning thedisruption of realistic stellar models. Our review surveys the immediateaftermath of disruption in both typical and more unusual TDEs, exploring howthe fate of the tidal debris changes if one considers non-main sequence stars,deeply penetrating tidal encounters, binary star systems, and sub-parabolicorbits. The stellar tidal disruption process provides the initial conditionsneeded to model the formation of accretion flows around quiescent massive blackholes, and in some cases may also lead to directly observable emission, forexample via shock breakout, gravitational waves or runaway nuclear fusion indeeply plunging TDEs.

The Process of Stellar Tidal Disruption by Supermassive Black Holes. The first pericenter passage