The proposed revision to the International System of Units contains two features that are bound to be of special interest to those concerned with foundational questions in philosophy of science. These are that the proposed system of international units (“New SI”) can be defined (a) without drawing a distinction between base units and derived units, and (b) without restricting (or even specifying) the means by which the value of the quantities associated with the units are to be established. In this chapter, I address the question of the role of base units in light of the New SI: Do the “base units” of the SI play any essential role anymore, if they are neither at the bottom of a hierarchy of definitions themselves, nor the only units that figure in the statements fixing the numerical values of the “defining constants”? The answer I develop and present (a qualified yes and no) also shows why it is important to retain the distinction between dimensions and quantities. I argue for an appreciation of the role of dimensions in understanding issues related to systems of units.