Sugarcane is the base of a successful agroindustrial system in several tropical and subtropical regions of the world. This industry is evolving towards diversification of its product portfolio and valorization of the vast amounts of lignocellulosic feedstocks: bagasse and straw. These trends make the sugarcane industry a learning ground for the utilization of agricultural residues and herbaceous biomass for bioenergy and biorefining. The presence of inorganics in sugarcane bagasse and straw, constitutive of the plant as well as originated from contamination, impacts several of the current and potential uses of the biomass. Although many studies refer broadly to terms like “inorganics”, “ash”, “silica”, “sand” or “mineral impurity”, there is a lack of a coherent and nuanced presentation of the inorganics of bagasse and straw: what they are, how variable they can be, and how they can impact different processes and products in biorefineries. This review article aims at filling this gap. Bagasse and straw inorganics are discussed considering their agroindustrial context and how they can impact processes such as combustion, pyrolysis, production of cellulosic ethanol and biomaterials. Prospects for valorization of the biomass inorganics are also discussed, beyond nutrient recycling. In the vision of this review, inorganics are not a marginal concern for biorefineries, as the percentage of inorganic content in biomass may seem to suggest. On the contrary, proper understanding and management of inorganics is key for the design of processes for advanced biorefineries.