In the present article, we review the recent neutron scattering studies on the anomalous behaviours found in the premartensitic bcc-based metals and alloys, i.e. alkali metals, group-IV metals, β-phase alloys, Ni-base alloys and others such as T1 and group-III metals. Lattice dynamical anomalies appearing on the [110]TA₁ and [111]LA phonon dispersion relations of these materials are discussed from a viewpoint of the martensitic transformation mechanism with referring briefly to theoretical studies. We also consider characteristics of anomalous elastic scatterings associated with the ω phase formation. Concerning these anomalies, we point out the importance of further examinations on the effects of vacancies, anharmonicity and electronic structure.