  Wormholes and black holes have traditionally been treated a quite separate
objects with relatively little overlap. The possibility of a connection arises
in that wormholes, if they exist, might have profound influence on black holes,
their event horizons, and their internal structure. After discussing some
connections, we embark on an overview of what can generally be said about
traversable wormhole throats. We discuss the violations of the energy
conditions that typically occur at and near the throat of any traversable
wormhole and emphasize the generic nature of this result. We discuss the
original Morris-Thorne wormhole and its generalization to a spherically
symmetric time-dependent wormhole, and also discuss spherically symmetric
Brans-Dicke wormholes. We also discuss the relationship with the topological
censorship theorem. Finally we turn to a rather general class of wormholes that
permit explicit analysis: generic static traversable wormholes (without any
symmetry). We define the wormhole throat in terms of a 2--dimensional
constant-time hypersurface of minimal area. (Zero trace for the extrinsic
curvature plus a ``flare--out'' condition.) This enables us to derive
generalized theorems regarding violations of the energy conditions---theorems
that do not involve geodesic averaging but nevertheless apply to situations
much more general than the spherically symmetric Morris-Thorne traversable
wormhole. [For example: the null energy condition (NEC), when suitably weighted
and integrated over the wormhole throat, must be violated.]
