Recent advances in the digitization of manufacturing have prompted ASME and International Organization for Standardization (ISO) standards committees to reexamine the definition of datums. Any new definition of datums considered by the standards committees should cover all datum feature types used in design and support both traditional metrological methods and new digital measurement techniques. This is a challenging task that requires some careful compromise. This paper describes and analyzes various alternatives considered by the standards committees. Among them is a new mathematical definition of datums based on constrained least-squares fitting. It seems to provide the best compromise and has the potential to support advanced manufacturing that is increasingly dependent on digital technologies.