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Two neutron stars merge somewhere in the Universe approximately every 10seconds, creating violent explosions observable in gravitational waves andacross the electromagnetic spectrum. The transformative coincidentgravitational-wave and electromagnetic observations of the binary neutron starmerger GW170817 gave invaluable insights into these cataclysmic collisions,probing bulk nuclear matter at supranuclear densities, the jet structure ofgamma-ray bursts, the speed of gravity, and the cosmological evolution of thelocal Universe, among other things. Despite the wealth of information, it isstill unclear when the remnant of GW170817 collapsed to form a black hole.Evidence from other short gamma-ray bursts indicates a large fraction ofmergers may form long-lived neutron stars. We review what is knownobservationally and theoretically about binary neutron star post-mergerremnants. From a theoretical perspective, we review our understanding of theevolution of short- and long-lived merger remnants, including fluid,magnetic-field, and temperature evolution. These considerations impactprospects of detection of gravitational waves from either short- or long-livedneutron star remnants which potentially allows for new probes into the hotnuclear equation of state in conditions inaccessible in terrestrialexperiments. We also review prospects for determining post-merger physics fromcurrent and future electromagnetic observations, including kilonovae andlate-time x-ray and radio afterglow observations.

The evolution of binary neutron star post-merger remnants: a review