Wave function-based quantum chemistry has two traditional lines of development – one based on molecular orbitals (MO's), and the other on valence bond (VB) theory. Both offer advantages and disadvantages for the challenging problem of describing strong correlations, such as the breaking of chemical bonds, or the low-spin (antiferromagnetic) coupling of electrons on different centers. Within MO methods, strong correlations can be viewed as those arising within a valence orbital active space. One reasonable definition of such a space is to supply one correlating orbital for each valence occupied orbital. Exact solution of the Schrodinger equation in this space is exponentially difficult with its size, and therefore approximations are imperative. The most common workaround is to truncate the number of orbitals defining the active space, and then solve the truncated problem, as is done in CASSCF. An important alternative is to systematically approximate the Schrödinger equation in the full valence space, for example by using coupled cluster theory ideas. I shall discuss progress in this direction. Within spin-coupled VB theory, the target wave function consists of a set of non-orthogonal orbitals, one for each valence electron, that are spin-coupled together into a state of the desired overall spin-multiplicity. The number of active orbitals is identical with the valence space MO problem discussed above, though the problem is not identical. Exact solution of the VB problem is exponentially difficult with molecular size, and therefore approximations are imperative. Again, the most common approach is to seek the exact solution in a truncated valence orbital space, where other orbitals are simply treated in mean-field. It is possible, however, to also consider approximations that do not truncate the space, but rather reduce the complexity. A new way of doing this will be introduced and contrasted with the MO-based approaches.