A review is given of recent neutron scattering studies of displacive incommensurate structures, and the instabilities that occur within periodic crystalline structures that lead to their formation. The concept of a soft phonon, in some cases associated with an electronic screening anomaly, is useful but not always capable of a completely satisfactory description. An unusual one-dimensional liquid-like phase has been studied in the non-stoichiometric mercury compound Hg 3-8 AsF 6.