The distinctive feature of tidally locked exoplanets is the very uneven heating by stellar radiation between the dayside and nightside. Previous work has focused on the role of atmospheric heat transport in preventing atmospheric collapse on the nightside for terrestrial exoplanets in the habitable zone around M dwarfs. In the present paper, we carry out simulations with a fully coupled atmosphere-ocean general circulation model to investigate the role of ocean heat transport in climate states of tidally locked habitable exoplanets around M dwarfs. Our simulation results demonstrate that ocean heat transport substantially extends the area of open water along the equator, showing a lobster-like spatial pattern of open water, instead of an "eyeball." For sufficiently high-level greenhouse gases or strong stellar radiation, ocean heat transport can even lead to complete deglaciation of the nightside. Our simulations also suggest that ocean heat transport likely narrows the width of M dwarfs' habitable zone. This study provides a demonstration of the importance of exooceanography in determining climate states and habitability of exoplanets.planetary climate | exoplanet habitability | superEarth M dwarf stars are the most common type of star in the Universe (1). The habitable zone (HZ) around M stars is close to such stars because of their weak luminosity (2). In consequence, habitable exoplanets orbiting M stars are likely to be tidally locked to their primary stars, so that one side of tidallocking exoplanets permanently faces stars, and the other side remains dark. Previous studies have demonstrated the role of atmospheric heat transport in preventing atmospheric collapse on the nightside of terrestrial exoplanets located in the HZ of M stars (3-10). For a planet with an extensive ocean, its climate and habitability also involves ocean heat transport, which is known to be important in Earth's climate (11). None of the existing studies has considered the role of ocean heat transport. Moreover, the climate also involves the spatial distribution of open water versus ice and the question of whether the planet becomes locked in a globally glaciated Snowball state. Simulation with a comprehensive Earth atmospheric general circulation model (AGCM) coupled to a slab ocean, without dynamic ocean heat transport, revealed an "eyeball" climate state, with a round area of open ocean centered at the substellar point and complete ice coverage on the nightside, even for very high CO 2 concentrations (4). In the presence of sea ice, ocean heat transport is likely to be especially important, because it is known from studies of the Snowball Earth phenomenon in Earth-like conditions that ocean heat transport is very effective in holding back the advance of the sea-ice margin (12-14). The distribution of sea ice on tidally locked exoplanets is only an issue for M stars, because planets with sufficiently dense atmospheres orbiting hotter stars in orbits close enough to yield tidal locking are likely to be too hot to permit ice and may ...