  Gravitational-wave (GW) astrophysics is a field in full blossom. Since the
landmark detection of GWs from a binary black hole on September 14th 2015,
several compact-object binaries have been reported by the LIGO-Virgo
collaboration. Such events carry astrophysical and cosmological information
ranging from an understanding of how black holes and neutron stars are formed,
what neutron stars are composed of, how the Universe expands, and allow testing
general relativity in the highly-dynamical strong-field regime. It is the goal
of GW astrophysics to extract such information as accurately as possible. Yet,
this is only possible if the tools and technology used to detect and analyze
GWs are advanced enough. A key aspect of GW searches are waveform models, which
encapsulate our best predictions for the gravitational radiation under a
certain set of parameters, and that need to be cross-correlated with data to
extract GW signals. Waveforms must be very accurate to avoid missing important
physics in the data, which might be the key to answer the fundamental questions
of GW astrophysics. The continuous improvements of the current LIGO-Virgo
detectors, the development of next-generation ground-based detectors such as
the Einstein Telescope or the Cosmic Explorer, as well as the development of
the Laser Interferometer Space Antenna (LISA), demand accurate waveform models.
[Abridged.]
