Well-reacted geopolymers with good compressive strengths (44-58 MPa) were formed from highly alkaline residue from red mud (the residue remaining after extraction of alumina from bauxite by the Bayer Process) without the addition of strength-promoting components, such as fly ash or ground slag, by adjusting the composition to an optimal SiO2/Al2O3 ratio of about 3 with silica fume. The formation of these geopolymers is extremely energy-efficient since thermal dehydroxylation of the red mud is not required. The environment of the Si and Al in the geopolymers was shown by Al-27 and Si-29 NMR spectroscopy to be consistent with reasonably well-reacted aluminosilicate materials, suggesting that the red mud forms geopolymers by reaction of aluminate and silicate species in a process not dissimilar to that of alkali-activated kaolin. The presence of high concentrations of iron in the red mud principally in the form of hematite did not interfere with geopolymer formation, since it was shown by XRD and Mossbauer spectroscopy to remain largely unaltered and not participate in the reaction. Analogous experiments with bauxite from which red mud is derived by alkali treatment, produce geopolymers of significantly lower strength (up to 28 MPa), suggesting that the action of the alkali during bauxite processing facilitates the formation of the geopolymer binder, possibly by increasing the reactivity of the red mud, as occurs in alkali-treated kaolinite.