[en] The density matrix expansion (DME) was originally introduced to establish contact between microscopic many-body theory based on a realistic two-body interaction and simplified phenomenological interactions of the Skyrme type. As a result of subsequent applications of the DME and simple phenomenological forces to deformed nuclei and problems in nuclear collective motion, several extensions to the original work are presented. The surface energy coefficient is shown to be -19.06 MeV when the spin-orbit and starting energy contributions are included, yielding excellent agreement with the semiempirical mass formula value of -18.56. The dominant effects of finite range are shown to be straightforwardly included in the direct Hartree term, and the Pauli operator is expressed in terms of the density matrix, yielding new insight into the local density approximation. Detailed comparisons are presented with Skyrme forces, and the density of states at the Fermi surface is shown to be reasonably well reproduced with the DME