  Originally regarded as forbidden, black hole ``hair'' are fields associated
with a stationary black hole apart from the gravitational and electromagnetic
ones. Several stable stationary black hole solutions with gauge or Skyrme field
hair are known today within general relativity. We formulate here a ``no
scalar--hair'' conjecture, and adduce some new theorems that almost establish
it by ruling out - for all but a small parameter range - scalar field hair of
spherical black holes in general relativity, whether the field be
self--interacting, coupled to an Abelian gauge field, or nonminimally coupled
to gravity.
