We compute by means of post-Newtonian (PN) methods the innermost stable circular orbit (ISCO) of compact binaries. Two methods are used, with equivalent results: one based on the equations of motion in harmonic coordinates and one on the Hamiltonian formalism in ADM coordinates. The ISCO is deduced from an invariant stability criterion, extending the 3PN criterion of Blanchet and Iyer (2003)...