Abstract: The last few years have seen a number of historic first detections in the field of gravitational waves. We now have dozens of detections across the range of masses. But what will be next? Will we have a gravitationally-lensed signal, or clear evidence of precession? Will we see a violation of General Relativity? I'll talk about how we find and measure these exotic systems, and especially how we can use new methods to deeply understand our data and make confident discoveries of previously unseen effects.