  I review the evolution of binary supermassive black holes and focus on the
stellar-dynamical mechanisms that may help to overcome the final-parsec problem
- the possible stalling of the binary at a separation much larger than is
required for an efficient gravitational wave emission. Recent N-body
simulations have suggested that a departure from spherical symmetry in the
nucleus of the galaxy may keep the rate of interaction of stars with the binary
at a high enough level so that the binary continues to shrink rather rapidly.
However, a major problem of all these simulations is that they do not probe the
regime where collisionless effects are dominant - in other words, the number of
particles in the simulation is still not sufficient to reach the asymptotic
behaviour of the system. I present a novel Monte Carlo method for simulating
both collisional and collisionless evolution of non-spherical stellar systems,
and apply it for the problem of binary supermassive black hole evolution. I
show that in triaxial galaxies the final-parsec problem is largely
non-existent, while in the axisymmetric case it seems to still exist in the
limit of purely collisionless regime relevant for real galaxies, but disappears
in the N-body simulations where the feasible values of N are still too low to
get rid of collisional effects.
