Coalescing binaries of compact objects (i.e. binary systems of black holes and/or neutron stars) are one of the most promising sources of gravitational waves (GWs) for a first detection with the upgraded LIGO-Virgo network of interferometers. The detection, identification, and accurate determination of the physical parameters of compact binary systems with GWs relies on the availability of accurate template banks of theoretical waveforms, which are filtered against the detector data.

For the inspiral part of the coalescence, when the two compact objects are still widely separated, analytical approximations to the gravitational waveforms can be obtained using the perturbative post-Newtonian (PN) approach. For the last orbits and the merger, where the fields are particularly strong, the full Einstein equations have to be solved numerically on supercomputers.

In this talk, I will discuss two ways in which information from PN and numerical relativity (NR) can be combined to produce accurate waveforms spanning the whole coalescence of the system. I will first focus on the construction of hybrid PN/NR waveforms for aligned-spin systems in the presence of "higher order modes" (subdominant spherical harmonics) which become relevant as the mass ratio of the system increases. I will then present the construction of a phenomenological inspiral-merger-ringdown model for the generic precessing case where the spins of the compact objects are misaligned with the orbital angular momentum of the system.