Improved estimates of dust aerosol effects upon climate require the characterization of the regional and temporal variability of dust mineral and chemical composition (which are typically assumed to be uniform in current climate models). Simulating the composition of dust aerosols in models is complicated because soil mineral grains and aggregates fragment during emission through saltation and sandblasting of the soil bed. These processes modify the size distribution and abundance of mineral phases of the emitted aerosols compared to the parent soil. An additional challenge for modeling is that global datasets of soil texture and composition are based on wet sieving, a technique that breaks the aggregates that are encountered in natural soils, drastically altering the original soil size distribution that is subject to wind erosion. We discuss two approaches to constrain the size distribution and mineral composition of emitted dust aerosols: an empirical method that uses measurements to constrain the size distribution of each mineral, and a theoretical method, which extends Kok's brittle fragmentation theory to individual minerals. In both cases, we also calculated aggregates between iron oxide minerals and other minerals to account for the transport of free iron to remote regions. We tested both approaches to predict the emission, transport, and deposition of dust minerals in the NASA GISS Earth System ModelE. We compared our regional distribution of minerals to that calculated using the common assumption that the emitted mineral composition is equal to the mineral composition of the soil. To evaluate our simulations we compiled a large dataset of mineral and elemental composition measurements. We discuss the improvements achieved with these new approaches and suggest future developments.