This paper reviews the results of recent molecular dynamics (MD) modelling studies of the interaction of water and solute species with mineral surfaces and their behaviour in mineral interlayers. Emphasis is on results for single and double hydroxide phases. Computational results are presented for water and anions in the interlayers of the Ca2Al, Mg2Al, and LiAl2 layered double hydroxides and on the surfaces of the Ca2Al phase. Detailed results for water on the (001) surface of brucite (Mg(OH)2) are presented and compared to published results for other phases. In all these cases, hydrogen bonding and the development of a hydrogen-bond network involving the H2O molecules and the solid substrate play very significant roles. The MD methods are especially effective for investigating the structure and dynamics of mineral-fluid interfaces and mineral interlayers, because they can be applied to systems containing hundreds to thousands of atoms and for extended durations of the order of nanoseconds.