This volume, the proceedings of IAU Symposium 363, addresses the astrophysical implications of gravitational wave and electromagnetic observations of neutron stars. It covers the state of the art understanding of mergers of binary neutron stars producing short gamma-ray bursts, and the most powerfully magnetic varieties of neutron stars, magnetars. Encapsulating both observations and modelling, the contributions address extreme transient events including kilonovae, afterglows, magnetar giant flares, and fast radio bursts. By exploring the intersection of studies of isolated neutron stars and binary system synthesis and merging, this collection sets the scene for interpreting exciting results pertaining to powerful x-ray, gamma-ray, and gravitational wave transients to be acquired in the next decade and beyond. IAU S363 will be an asset for astronomers seeking a broad and interdisciplinary overview of neutron stars, their gravitational waves and electromagnetic emission.