  We derive the conservative dynamics of non-spinning binaries to third
Post-Minkowskian order, using the Effective Field Theory (EFT) approach
introduced in [2006.01184] together with the Boundary-to-Bound dictionary
developed in [1910.03008, 1911.09130]. The main ingredient is the scattering
angle, which we compute to ${\cal O}(G^3)$ via Feynman diagrams. Adapting to
the EFT framework powerful tools from the amplitudes program, we show how the
associated (master) integrals are bootstrapped to all orders in velocities via
differential equations. Remarkably, the boundary conditions can be reduced to
the same integrals that appear in the EFT with Post-Newtonian sources. For the
sake of comparison, we reconstruct the Hamiltonian and the classical limit of
the scattering amplitude. Our results are in perfect agreement with those in
Bern et al. [1901.04424, 1908.01493].
