We review the use of elemental depletions in determining the composition of interstellar dust and present a new interpretation of the elemental depletion patterns for the dust forming elements in a range of diffuse cloud types. We discuss this within the context of dust processing in the interstellar medium and show that Si and Mg are selectively eroded from dust, with respect to Fe, as expected for a sputtering erosion process. However, we find that Si is preferentially and nonstoichiometrically eroded from dust with respect to Mg by some as yet unidentified process that may act in conjunction with grain sputtering. On this basis a new way of interpreting the depletions in terms of continuous dust processing through erosion in the interstellar medium is presented. The observed depletion patterns can then be understood in terms of a gradually changing grain chemical composition as the erosion of the atoms proceeds nonstoichiometrically in the low-density interstellar medium. The stoichiometric erosion of multicomponent (e.g., core/mantle) single grains can qualitatively explain the observed depletions but is not consistent with the preferential erosion of Si from dust. We present suggestions for the usage of mineralogical terms within the context of interstellar and circumstellar dust mineralogy. ¿ 2000 American Geophysical Union