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We present simulations of atmospheres of Earth‐like aquaplanets that are tidally locked to their star, that is, planets whose orbital period is equal to the rotation period about their spin axis, so that one side always faces the star and the other side is always dark. Such simulations are of interest in the study of tidally locked terrestrial exoplanets and as illustrations of how planetary rotation and the insolation distribution shape climate. As extreme cases illustrating the effects of slow and rapid rotation, we consider planets with rotation periods equal to one current Earth year and one current Earth day. The dynamics responsible for the surface climate (e.g., winds, temperature, precipitation) and the general circulation of the atmosphere are discussed in light of existing theories of atmospheric circulations. For example, as expected from the increasing importance of Coriolis accelerations relative to inertial accelerations as the rotation rate increases, the winds are approximately isotropic and divergent at leading order in the slowly rotating atmosphere but are predominantly zonal and rotational in the rapidly rotating atmosphere. Free‐atmospheric horizontal temperature variations in the slowly rotating atmosphere are generally weaker than in the rapidly rotating atmosphere. Interestingly, the surface temperature on the night side of the planets does not fall below ∼240 K in either the rapidly or slowly rotating atmosphere; that is, heat transport from the day side to the night side of the planets efficiently reduces temperature contrasts in either case. Rotational waves and eddies shape the distribution of winds, temperature, and precipitation in the rapidly rotating atmosphere; in the slowly rotating atmosphere, these distributions are controlled by simpler divergent circulations. Both the slowly and rapidly rotating atmospheres exhibit equatorial superrotation. Systematic variation of the planetary rotation rate shows that the equatorial superrotation varies non‐monotonically with rotation rate, whereas the surface temperature contrast between the day side and the night side does not vary strongly with changes in rotation rate.