Rapidly-rotating neutron stars are observed in multiple electromagnetic wavebands, and may also emit gravitational waves detectable with current-generation interferometric detectors. These objects can be utilised to probe fundamental physical theories in extreme environments; the disk-magnetosphere interaction; and the properties of matter under extreme conditions. Significant progress has been made in this field in recent years, including the first detection of 'transitional' objects bridging the gap between rotation- and accretion-powered pulsars, and the recent discovery of a neutron star - neutron star merger. The possible constraints on the neutron star equation of state from such mergers, as well as from X-ray timing and spectral observations, are likely the most stringent available, provided the many systematic effects can be quantified. This event will cover the current status, including new theoretical and multi-wavelength observational results, and future directions of this rapidly-developing field.