The International System of Units (SI) is a coherent system based originally on measurements of properties of material objects. In more recent times, the adopted definitions depend on setting values of universal constants wherever possible. The last remaining human-made material object on which a standard is based is a platinum-iridium kilogram located in Sevres, France. The International Bureau of Weights and Measures is considering replacing this physical object as the standard and tying all base units to physical constants that are fixed. The reasons will be explicated in this paper. (Contains 1 figure.)