  Objects that are on the verge of being extremal black holes but actually are
distinct in many ways are called quasi-black holes. Quasi-black holes are
defined here and treated in a unified way through the displaying of their
properties. The main ones are (i) there are infinite redshift whole regions,
(ii) the spacetimes exhibit degenerate, almost singular, features but their
curvature invariants remain perfectly regular everywhere, (iii) in the limit
under discussion, outer and inner regions become mutually impenetrable and
disjoint, although, in contrast to the usual black holes, this separation is of
a dynamical nature, rather than purely causal, (iv) for external far away
observers the spacetime is virtually indistinguishable from that of extremal
black holes. It is shown, in addition, that quasi-black holes must be extremal.
Connections with black hole and wormhole physics are also drawn.
