  In this work, we review the effective field theory framework to search for
Lorentz and CPT symmetry breaking during the propagation of gravitational
waves. The article is written so as to bridge the gap between the theory of
spacetime-symmetry breaking and the analysis of gravitational-waves signals
detected by ground-based interferometers. The primary physical effects beyond
General Relativity that we explore here are dispersion and birefringence of
gravitational waves. We discuss their implementation in the open-source
LIGO-Virgo algorithm library suite, as well as the statistical method used to
perform a Bayesian inference of the posterior probability of the coefficients
for symmetry-breaking. We present preliminary results of this work in the form
of simulations of modified gravitational waveforms, together with sensitivity
studies of the measurements of the coefficients for Lorentz and CPT violation.
The findings show the high potential of gravitational wave sources across the
sky to probe sensitively for these signals of new physics.
