  This article outlines the search for an exact general relativistic
description of the exterior (vacuum) gravitational field of a rotating
spheroidal black hole surrounded by a realistic axially symmetric disc of
matter. The problem of multi-body stationary spacetimes is first exposed from
the perspective of the relativity theory and astrophysics, listing the basic
methods employed and results obtained. Then, basic formulas for stationary
axisymmetric solutions are summarized. Remaining sections review what we have
learnt with Miroslav Zacek and Tomas Zellerin about certain static and
stationary situations recently. Although the survey part is quite general, the
list of references cannot be complete. Our main desideratum was the informative
value rather than originality -- novelties have been preferred, mainly reviews
and those with detailed introductions.
