ABSTRACT: Gravitational-wave detectors are yielding a bounty of observations, and revolutionising our understanding of stellar-mass black holes. But what about the supermassive black holes that lurk at the heart of massive galaxies? These titans form binaries over cosmic time as a byproduct of hierarchical galaxy growth, emanating gravitational waves in the nanohertz sensitivity band of networks of Milky Way millisecond pulsars. Pulsar-timing arrays (PTAs) like the North American Nanohertz Observatory for Gravitational waves (NANOGrav) are poised to chart this new frontier of gravitational wave discovery within the next several years. With this new window onto the warped Universe, PTAs will bring a sea-change in our understanding of supermassive binary black-hole demographics and dynamical interactions. Combined with electromagnetic signatures of binary AGN in upcoming time-domain synoptic surveys, PTAs will extend the arena of multi-messenger astronomy to the most massive black holes in the Universe. Additionally, pulsar-timing arrays are currently placing compelling constraints on modified gravity theories, cosmic strings, and ultralight scalar-field dark matter. I will review the current status of PTA searches, and present some milestones on the road to the exciting next decade and beyond of PTA discovery.