Recent achievements in the Hamiltonian treatment of the dynamics and motion of compact binaries in general relativity

The current knowledge in the post-Newtonian (PN) dynamics and motion of non-spinning and spinning compact binaries will be presented based on the Arnowitt-Deser-Misner Hamiltonian approach to general relativity. The presentation will cover the binary dynamics with non-spinning components up to the 4PN order and for spinning binaries up to the next-to-next-to-leading order in the spin-orbit and spin-spin couplings. Radiation reaction will be treated for both non-spinning and spinning binaries. Explicit analytic expressions for the motion will be given, innermost stable circular orbits will be discussed