The first observation of gravitational waves opened unprecedented avenues to probe the physics of gravity. For this, accurate models of these wave signals are crucial. The latter are typically assumed to propagate in a vacuum, isotropic and expanding Universe in which individual sources reside. This works refines that assumption, considering the presence of physical structures in the Universe. We target specific effects affecting signals for both ground-based, space-based interferometers, and pulsar timing arrays. With gravitational lensing, we show the effect of the presence of structures on path of the waves, with an emphasis on wave optics phenomena and the black hole lens. We also consider kinematic and clustering anisotropies globally affecting source populations. All of these are imprints left by a realistic Universe on gravitational wave signals. This shall eventually be exploited both for the purpose of refining signal models, and to strengthen our understanding of the Universe’s properties.