The discovery of strong gravitational lensing of gravitational waves (GWs) would represent a major advance in astronomy. Assessing the probability that two or more events are lensed images of the same source requires a good understanding of the properties of the lensed images. In this talk I will discuss the key role of lensing phase shifts. Contrary to electromagnetic radiation intuition, lensing phase shifts could distort the GW waveform so that it differs from the (unlensed) general relativity prediction. I will quantify how relevant these distortions are for current GW detectors and outline an optimal lensing search strategy. Next, I will present the prospects of testing theories beyond general relativity with GW lensing, discussing novel effects such as GW birefringence, echoes and shadows
