Progress in understanding electronic correlation is reviewed over a period of some 40 years, taking the point of view that understanding is incomplete unless it is embodied in computational theory capable of quantitative predictions of experimental data. Some of the numerous successes of such theory are reviewed, but principal emphasis is placed on the remaining gap between MCSCF-CI methods capable of accurate results for atoms and small molecules and methods suitable for large systems. These latter methods have generally relied on effective one-electron Hamiltonians, as in local density functional theory, which model the effects of electronic correlation. Despite the great practical importance of such methods, they have limitations in dealing with electronic correlation that are difficult to assess within the conceptual framework of the theory. Current ideas that may help to close this gap are discussed. © 1990 American Chemical Society.