The relationships between molecular structure and the nonlinear optical phenomenon second-harmonic generation (SHG) are discussed. New-found relationships built up from basic structural axioms that were deduced in the 1970s and 1980s are the particular focus of this article, using structural results from X-ray and neutron-diffraction studies. The molecular and supramolecular manifestations of the SHG effect are borne out, although ways to optimize the effect on the molecular scale feature predominantly, since control of SHG on the supramolecular scale remains difficult given present limitations. The use of a variety of templates to generate head-to-tail oriented host-guest species thereby bypassing such limitations is described. The paper concludes with a look ahead at next generation 'octupolar' SHG-active compounds, the prediction of new series of SHG-active compounds via data-mining computational procedures, and developments in diffraction technology that may enable structural movies of a molecule to be captured during the SHG process. A practical assessment of the viability of organic SHG materials for industrial application is reviewed with a positive outcome, thus indicating a promising future for organic SHG materials.