Mineral dust particles suspended in the atmosphere span more than three orders of magnitude in diameter, from less than 0.1 µm to more than 100 µm. This wide size range makes dust a unique aerosol species with the ability to interact with many aspects of the Earth system, including radiation, clouds, hydrology, atmospheric chemistry, and biogeochemistry. This review focuses on coarse and super-coarse dust aerosols, which we respectively define as dust particles with a diameter between 2.5 - 10 µm and 10 - 62.5 µm. We review several lines of observational evidence indicating that coarse and super-coarse dust particles are transported farther than previously expected and that the abundance of these particles is substantially underestimated in current global models. We synthesize previous studies that used observations, theories, and model simulations to highlight the impacts of coarse and super-coarse dust aerosols on the Earth system, including their effects on dust-radiation interactions, dust-cloud interactions, and atmospheric chemistry, and biogeochemistry. In addition, we examine several limitations in the representation of coarse and super-coarse dust aerosols in current model simulations and in remote-sensing retrievals. Because these limitations substantially contribute to the uncertainties in simulating the abundance and impacts of coarse and super-coarse dust aerosols, we offer some recommendations to facilitate future studies. Overall, we conclude that an accurate representation of coarse and super-coarse properties is critical in understanding the overall impacts of dust aerosols on the Earth system.