Gravitational waves (GWs) are reshaping our understanding of the universe, and the more exciting discoveries are yet to come. In the next observing runs we will observe hundreds to thousands of events per year at increasingly higher redshifts, opening unique opportunities to test our cosmological model. In this talk I will focus on how this coming data could help probing gravity and dark energy, and what new information GW lensing will provide. In the first part of the talk I will describe how, without the need for electromagnetic counterparts or galaxy catalogs, the study of the binary black hole mass distribution can constrain LCDM and Einstein’s gravity. Moreover, I will show that black hole mergers are also promising laboratories to bound GW interactions with other cosmological fields leading to waveform distortions and echoes. In the second part, I will discuss current searches for strongly lensed GWs and the importance of the GW phase measurement in this identification. Observing GW lensed events will allow us to probe the matter distribution in the universe and further constrain the laws of gravity. In both parts of the talk I will emphasize the important role of next generation ground- and space-based detectors.