  A unified approach to regular interiors of black holes with smooth matter
distributions in the core region is given. The approach is based on a class of
Kerr-Schild metrics representing minimal deformations of the Kerr-Newman
solution, and allows us to give a common treatment for (charged and uncharged)
rotating and nonrotating black holes. It is shown that the requirement of
smoothness of the source constraints the structure of the core region in many
respects: in particular, for Schwarzschild holes a de Sitter core can be
selected, which is surrounded by a smooth shell giving a leading contribution
to the total mass of the source. In the rotating, noncharged case the source
has a similar structure, taking the form of a (anisotropic and rotating) de
Sitter-like core surrounded by a rotating elliptic shell. The Kerr singular
ring is regularized by anisotropic matter rotating in the equatorial plane, so
that the negative sheet of the Kerr geometry is absent. In the charged case the
sources take the form of ``bags'', which can have de Sitter or anti de Sitter
interiors and a smooth domain wall boundary, with a tangential stress providing
charge confinement. The ADM and Tolman relations are used to calculate the
total mass of the sources.
