  Recently, different methods succeeded in calculating the spin dynamics at
higher orders in the post-Newtonian (PN) approximation. This is an essential
step toward the determination of more accurate templates for gravitational
waves, to be used in future gravitational wave astronomy. We focus on the
extension of the ADM canonical formalism to spinning binary black holes. Using
the global Poincare invariance of asymptotically flat spacetimes as the most
important guiding consistency condition, this extension can be constructed
order by order in the PN approximation. We were able to reach a high order both
in the spin power and the PN counting.
