Wave functions featuring both short-range strong electron correlation in multiple distinct, localized centers as well as long-range weaker electron correlation are ideal targets for electronic structure methods based on two-step diagonalization of the molecular Hamiltonian. Two-step diagonalization means that the molecular Hamiltonian is first diagonalized in several localized subspaces, and then a selection of localized eigenstates (which we call "fragment statelets") are multiplied together across the fragments to generate a space of whole-system "model states." In the second step, the Hamiltonian is projected into and diagonalized within this model space. Methods such as active space decomposition, vector product state (VPS)-CASCI or VPS-CASSCF, and tensor product state selected CI (TPSCI) use two-step diagonalization.