Commission 4 (Ephemerides) of the International Astronomical Union (IAU) includes astronomers from many countries responsible for the production of printed almanacs, software, and web services that provide basic data on the positions and motions of celestial objects, and the times of phenomena such as rise and set, eclipses, phases of the Moon, etc. This information is important for pointing telescopes, determining optimal times for observations, conducting night operations, and also for celestial navigation. Commission 4 also includes researchers involved in the more fundamental tasks of determining the orbits of solar system bodies based on a variety of observations taken from the ground and spacecraft. We assume that the data we produce are used by a variety of people that have a broad range of scientific sophistication. In the almanacs, software, and web services that Commission 4 members produce, data that are independent of the rotation of the Earth, such as the geocentric celestial coordinates (right ascension and declination) of the Sun, Moon, planets, and stars, are generally provided as a function of Terrestrial Time (TT). In practice, TT is based on atomic time (TT=TAI+32.184s) and as such, it can be extended indefinitely into the future without ambiguity or error. On the other hand, data that depend on the rotation of the Earth, such as Greenwich hour angles or the topocentric coordinates (zenith distance and azimuth) of celestial objects, have traditionally been provided as a function of Universal Time, specifically UT1. UT1 is inherently unpredictable because of natural irregularities in the length of day, but the current international time protocol guarantees that UTC, the basis for civil time worldwide, is never more than 0.9 seconds from UT1. For many users and software applications, the approximation UT1=UTC is adequate and is assumed. Many users, particularly navigators, are probably not even aware of the distinction between UTC and UT1. A change in the definition of UTC that allows it to diverge from UT1 without bound therefore creates a challenge as to how to provide future data that are a function of the rotational angle of the Earth, and how to educate users on the change. Several ideas for how to proceed that have been circulating among Commission 4 members will be explored.