Gravitational lensing offers a powerful tool for exploring the matter distribution in the Universe. Thanks to their low frequencies and phase coherence, gravitational waves (GWs) allow for the observation of novel wave-optic features (WOFs) in lensing, which are inaccessible to electromagnetic signals. Combined with the existing accurate source models, lensed GWs can be used to infer the properties of gravitational lenses. The prospect is particularly compelling for space-borne detectors, where the high signal-to-noise ratio expected from massive black hole binary mergers allows WOFs to be distinguished deep into the weak lensing regime, drastically increasing the detection probability. I will talk about the capacity of the LISA mission in the milli-Hz regime to detect WOFs caused by dark matter halos, galaxies and the supermassive black holes within them, The prospect of observing WOFs is very sensitive to the central concentrations of the dark-matter halos, and in general to the lens profiles. I will also discuss how the lensing probabilities look for other proposed spaced-based GW detectors like muAres (micro-Hz), DO (deci-Hz) etc. suggesting that in the future GW lensing will be an excellent probe of dark-matter theories, baryonic and halo sub-structures. If time allows, I will also briefly discuss the observational prospects of the WOFs due to stellar and intermediate-mass black holes in the current and 3G ground-based detectors