Abstract. Gravitational waves can probe cosmic structures via gravitational lensing in ways that are highly complementary to electromagnetic signals: 1) their low frequency and phase coherence makes them sensitive to wave-optics diffraction and frequency-dependent effects, 2) weak interactions with matter allow them to probe dense regions, such as the cores of galactic halos and 3) accurate waveform models provide an additional handle to pinpoint lensing effects.

I will first review the gravitational lensing of gravitational waves and discuss how lensing signals can be computed and modeled. Afterwards, I will describe how strongly-lensed LVK and LISA events can probe properties of Dark Matter halos, such as the radial slope of the density and the existence of a central core.

These unique signatures will enable novel probes of fundamental physics and astrophysics in galactic centers.