It is now possible to obtain indirect values of the Avogadro constant NA having comparatively small combined standard uncertainties by appropriately combining the values of a number of other fundamental physical constants. These constants, whose values in several important cases can be obtained from electrical measurements, include the Rydberg, fine-structure, Josephson, von Klitzing, Planck, and Faraday constants, the molar mass of the proton, the proton-electron mass ratio, and the shielded proton gyromagnetic ratio. This paper gives the expressions that relate NA to these other fundamental constants and the values of NA that can be obtained from these expressions using the currently available data. It also briefly discusses the prospects of obtaining an indirect value of NA with a combined standard uncertainty that is small enough to allow the redefinition of the kilogram.