Recent proposals to fundamentally change the international system of units (SI) have generated considerable debate and are now being seriously considered by international committees. These proposals have a common theme—to exactly fix the values of a set of fundamental physical constants and to then base the SI units with respect to these invariant constants. This article will summarize the proposed changes and outline how national standards institutes would typically realize the SI units within the new system. The expected benefits and drawbacks of these changes will be summarized as they pertain to measurement science and fundamental constants. The official positions of different metrological communities as well as possible time schedules and the approval process that must be followed to implement such changes to the SI will be outlined.