Physical measurements depend on an evolving structure of base units, algorithms for their realization, and recommended procedures that constitute the International System of Units (SI). Until the second half of the twentieth century, most such base units were defined in terms of specific physical artifacts. These units entered the measurement process by means of replicas of the primary artifacts. Much work has been done to replace these artifact standards by invariant alternatives, such as atomic transition frequencies and fundamental physical constants. Only the base unit of mass remains defined by an artifact. Efforts involving atom counting and electromagnetic force generation may provide an invariant replacement.