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