The ability to directly observe gravitational waves will open up unprecedented scientific opportunities at the interface of astronomy, astrophysics, fundamental physics, and cosmology. Gravitational and classical astronomy will together observe highly energetic and transient phenomena in the Universe. The goal of the workshop is twofold: (1) to explore how upcoming observations of such processes can help us understand physics at the extreme - strong gravitational fields as well as ultra-high densities, temperatures and magnetic fields - and (2) to discuss the ultimate science goals for this emerging, synergistic field, and what future detectors and telescopes will be needed to make a step change in the scientific questions we can address.