The low-energy, low-spin collective modes of nuclei that can be excited through inelastic scattering reactions with fast neutrons are reviewed. Recent studies of quadrupole, octupole, and multiphonon vibrations are described, and more exotic modes, including mixed-symmetry states, scissors mode states, and intruder excitations, are presented. The opportunities afforded through reactions with very energetic neutrons are considered, and a view to the future of nuclear structure studies with energetic neutrons is given.