The diets of over two-thirds of the world's population lack one or more essential mineral elements. This can be remedied through dietary diversification, mineral supplementation, food fortification, or increasing the concentrations and/or bioavailability of mineral elements in produce (biofortification). This article reviews aspects of soil science, plant physiology and genetics underpinning crop biofortification strategies, as well as agronomic and genetic approaches currently taken to biofortify food crops with the mineral elements most commonly lacking in human diets: iron (Fe), zinc (Zn), copper (Cu), calcium (Ca), magnesium (Mg), iodine (I) and selenium (Se). Two complementary approaches have been successfully adopted to increase the concentrations of bioavailable mineral elements in food crops. First, agronomic approaches optimizing the application of mineral fertilizers and/or improving the solubilization and mobilization of mineral elements in the soil have been implemented. Secondly, crops have been developed with: increased abilities to acquire mineral elements and accumulate them in edible tissues; increased concentrations of ‘promoter’ substances, such as ascorbate, β-carotene and cysteine-rich polypeptides which stimulate the absorption of essential mineral elements by the gut; and reduced concentrations of ‘antinutrients’, such as oxalate, polyphenolics or phytate, which interfere with their absorption. These approaches are addressing mineral malnutrition in humans globally.