  Event Horizon, a null hypersurface defining the boundary of the black hole
region of a spacetime, is not particularly useful for evolving black holes
since it is non-local in time. Instead, one uses the more tangible concept of
Apparent Horizon for dynamical black holes out there in the sky that do all
sorts of things: evolve, merge and feed on the environment. Event Horizon,
being a gauge-independent, global property of the total spacetime is easy to
define and locate in the stationary case; on the other hand, Apparent Horizon
depends on the embedding of the surface in spacetime and hence it is somewhat
tricky to define. But for numerical simulations in General Relativity, locating
the Apparent Horizon helps one to excise the black hole region and the
singularity to have a stable computation. Moreover, for stationary solutions
the two horizons match. Here we give a detailed pedagogical exposition of the
subject and work out the non-trivial case of a slowly moving and spinning black
hole.
