Waveform modeling is at the core of gravitational-wave astronomy: waveform templates are required for both detecting signals and extracting astrophysical information via parameter estimation. For compact binary sources, waveform modeling requires the solution of the general-relativistic (GR) two-body problem which is of renewed and central importance in the gravitational-waves era. This talk presents a state-of-art effective one body framework (TEOBResumS) to model the motion of arbitrary compact binaries on arbitrary orbits and it showcases two main applications. For binary black holes, I discuss the first GR predictions of hyperbolic mergers under radiation reaction and the transition between scattering and bound orbits. These results prompted the interpretation of GW190521 as the first dynamical capture of stellar mass black holes observed. For binary neutron stars, I discuss the first model for the complete gravitational-wave spectrum (at all the frequencies). As primary application, the model will allow to infer constraints on the mass-radius diagram of neutron stars and nuclear matter with third generation detectors.