The kilogram, the base unit of mass in the International System of Units (SI), is defined as the mass m(K) of the international prototype of the kilogram. Clearly, this definition has the effect of fixing the value of m(K) to be one kilogram exactly. In this paper, we review the benefits that would accrue if the kilogram were redefined so as to fix the value of either the Planck constant h or the Avogadro constant N A instead of m(K), without waiting for the experiments to determine h or N A currently underway to reach their desired relative standard uncertainty of about 10 −8 . A significant reduction in the uncertainties of the SI values of many other fundamental constants would result from either of these new definitions, at the expense of making the mass m(K) of the international prototype a quantity whose value would have to be determined by experiment. However, by assigning a conventional value to m(K), the present highly precise worldwide uniformity of mass standards could still be retained. The advantages of redefining the kilogram immediately outweigh any apparent disadvantages, and we review the alternative forms that a new definition might take.