  We describe efforts over the last six years to implement regularization
methods suitable for studying one or more interacting black holes by direct
N-body simulations. Three different methods have been adapted to large-N
systems: (i) Time-Transformed Leapfrog, (ii) Wheel-Spoke, and (iii) Algorithmic
Regularization. These methods have been tried out with some success on
GRAPE-type computers. Special emphasis has also been devoted to including
post-Newtonian terms, with application to moderately massive black holes in
stellar clusters. Some examples of simulations leading to coalescence by
gravitational radiation will be presented to illustrate the practical
usefulness of such methods.
