The single-particle potentials for nucleons and hyperons in neutron-rich matter generally depends on the density and isospin asymmetry of the medium as well as the momentum and isospin of the particle. It further depends on the temperature of the matter if the latter is in thermal equilibrium. We review here the extension of a Gogny-type isospin- and momentum-dependent interaction in several aspects made in recent years and their applications in studying intermediate-energy heavy ion collisions, thermal properties of asymmetric nuclear matter and properties of neutron stars. The importance of the isospin- and momentum-dependence of the single-particle potential, especially the momentum dependence of the isovector potential, is clearly revealed throughout these studies. ; Comment: 27 pages, 19 figures, 1 table, accepted version to appear in EPJA special volume on Nuclear Symmetry Energy