This great success of DFT can be favourably compared with a rather tumultuous development of "higher-order" full 1RDM or density-matrix-functional (DMFT) and 2RDM theories, which still do not enjoy a truly successful "take-off". The ongoing development (see contribution (4.1.1)) explores a way in which DFT can help DMFT with such a "take-off", while DMFT can help DFAs with the problematic inclusion in the latter of nondynamical or strong electron correlation.