  A brief, and certainly not exhaustive, survey is provided of some recent
results and conjectures in four and higher spacetime dimensions, such as the
Hoop Conjecture, relating the geometry of event horizons to dynamical
quantities such as the total energy or mass of the spacetime containng the
black hole. As a measure of the size of a hoop one may take Birkhoff's
invariant based on sweepouts by circles or higher dimensional analogues or one
may take the length of the shortest non-trivial closed geodesic. Also discussed
are whether one can hear the shape of a black hole and to what extent one may
associate with it a volume.
