The recent detection of gravitational waves (GWs) in 2015 opened a completely new way to constrain cosmology and gravity. In this thesis, I start by reviewing how gravitational waves emitted by compact binaries may be used as distance indicators in the context of general relativity. I then discuss scalar-tensor modifications of gravity motivated as dark-energy models and how those can affect gravitational waves and evade local constraints from the Solar System via so-called screening mechanisms. In particular, I present how the effective distance probed by standard sirens may be affected by scalar-tensor modifications of gravity. I show how this distance is only affected by local properties of the source and of the observer, which are assumed and constrained to live in screened environments. To do so, I present a formalism to study the evolution of the amplitude of scalar and tensor waves which propagate in a generically curved background spacetime, which allows to account for inhomogeneities which appear in the Universe, as well as in the background scalar field, necessary to account for screening. I present a way to diagonalize the system of equations of motion for the scalar and tensor degrees of freedom and find that interactions are always negligible, although the argument depends on the scalar phase velocity. Next, I focus on subluminal scalar waves interacting with matter fields and discuss scalar Cherenkov radiation from high-energy cosmic rays, which may slow them down. I show how this effect is negligible if the effective field theory (EFT) of gravity is designed to explain cosmic acceleration but how it may be significant if the EFT is applicable at higher energy scales. Finally, I challenge the geometric optics approximation in a general relativistic GW lensing scenario. I show how in certain configurations, a point-like lens can affect the transport of the polarization of the gravitational waves in such a way that may be confused with a smoking gun signature of deviations from general relativity. I discuss the probability to generate significant effective non-tensorial polarizations in a realistic Universe and find that the probability is small for the expected binary black hole merger rates, thereby confirming the robustness of the geometric optics approximation.