Predictive geometallurgy tries to optimize the mineral value chain based on a precise and quantitative understanding of: the geology and mineralogy of the ores, the minerals processing, and the economics of mineral commodities. This chapter describes the state of the art and the mathematical building blocks of a possible solution to this problem. This solution heavily relies on all classical fields of mathematical geosciences and geoinformatics, but requires new mathematical and computational developments. Geometallurgy can thus become a new defining challenge for mathematical geosciences, in the same fashion as geostatistics has been in the first 50 years of the IAMG.Geometallurgy, from the Greek words for earth (geia), metal (metallo) and work (ergon), can be understood as the exploitation of a metallic ore based on a precise understanding of its geoscientific characteristics. Geometallurgy is hence a cooperation field for geoscientists and mineral processing engineers, something which has occurred in virtually all mining operations. A modern understanding of geometallurgy, what we could call predictive geometallurgy, proposes a quantitative approach to the subject. In rough terms, that requires optimizing the ore processing based on automated mineralogy and microstructure characterisation of the ore, coupled with geometallurgical tests. These are tests conducted at several scales (from lab to plant) along which the actual ore is processed in realistic conditions in order to study the differential behaviour of the several ore and waste mineral phases, and thus the enriching potential of the ore through the processes considered.