Clay minerals find a wide range of application in composites, paints, drilling liquids, cosmetics, and medicine. This article reviews chemical and physical properties of natural and organically modified clay minerals to understand the nanometre-scale structure, surface characteristics, and application in functional materials. The relation between fundamental properties and materials design is emphasized and illustrated by examples. The discussion comprises the following: an overview; surface structure and cation density; solubility and solubility reversal by surface modification; the degree of covalent and ionic bonding represented by atomic charges; the distribution of metal substitution sites; measurements and simulations of interfacial properties at the nanometre scale; self-assembly, packing density, and orientation of alkylammonium surfactants on the clay mineral surface; the density and chain conformation of surfactants in organic interlayer spaces; the free energy of exfoliation in polymer matrices and modifications by tuning the cleavage energy; thermal transitions, diffusion, and optical responses of surfactants on the mineral surface; elastic moduli and bending stability of clay layers; and the adsorption mechanism of peptides onto clay mineral surfaces in aqueous solution. Potential applications in biotechnology and other future uses are described.