  The critical steps leading to the uniqueness theorem for the Kerr-Newman
metric are reexamined in the light of the new black hole solutions with
Yang-Mills and scalar hair. Various methods -- including scaling techniques,
arguments based on energy conditions, conformal transformations and divergence
identities -- are reviewed, and their range of application to selfgravitating
scalar and non-Abelian gauge fields is discussed. In particular, the no-hair
theorem is extended to harmonic mappings with arbitrary Riemannian target
manifolds. (This paper is an extended version of an invited lecture held at the
Journ\'ees Relativistes 96.)
