The gravitational-wave window onto the universe will open in roughly five years, when Advanced LIGO and Virgo achieve the first detections of high-frequency gravitational waves, most likely coming from compact binary mergers. Electromagnetic follow-up of these triggers, using radio, optical, and high energy telescopes, promises exciting opportunities in multi-messenger time-domain astronomy. In the decade, space-based observations of low-frequency gravitational waves from massive black hole mergers, and their electromagnetic counterparts, will open up further vistas for discovery. This two-part workshop featured brief presentations and stimulating discussions on the challenges and opportunities presented by gravitational-wave astronomy. Highlights from the workshop, with the emphasis on strategies for electromagnetic follow-up, are presented in this report.