  Supermassive black holes can capture or disrupt stars that come sufficiently
close. This article reviews the dynamical processes by which stars or stellar
remnants are placed onto loss-cone orbits and the implications for feeding
rates. The capture rate is well defined for spherical galaxies with nuclear
relaxation times that are shorter than the galaxy's age. However, even the
dense nucleus of the Milky Way may be less than one relaxation time old, and
this is certainly the case for more massive galaxies; the capture rate in such
galaxies is an initial-value problem with poorly-known initial conditions and
the rate can be much higher, or much lower, than the rate in a collisionally
relaxed nucleus. In nonspherical (axisymmetric, triaxial) galaxies, torquing of
orbits by the mean field can dominate perturbations due to random encounters,
leading to much higher capture rates than in the spherical geometry,
particularly in (massive) galaxies with long central relaxation times.
Relativistic precession plays a crucial role in mediating the capture of
compact remnants from regions very near to the black hole, by destroying the
orbital correlations that would otherwise dominate the torques. The complex
dynamics of relativistic loss cones are not yet well enough understood for
accurate estimates of compact-object (EMRI) capture rates to be made.
