Because the molecular Hamiltonian contains only one-body and two-body operators, the two-electron reduced density matrix contains all the information needed to evaluate the energy, as well as most of the other properties of interest to chemists and molecular physicists. A straightforward minimization of the energy is confounded by the N-representability problem, which can only be addressed approximately. The resulting theory has both advantages and disadvantages compared to more traditional wavefunction-based approaches. The biggest advantage is that it performs well even when the molecule of interest has strong multireference character and the “Hartree-Fock plus correction” wavefunction paradigms fail. Also, as a lower-bound method, it provides a complementary tool to variational wavefunction approaches. The biggest disadvantages are the computational cost (which may yet be surmounted) and problems with dissociation and degeneracy that seem to afflict all approaches based on a “reduced” description of the system.