This perspective describes research, carried out in the authors' labs over the past forty years, aimed at understanding, predicting, and measuring the singlet–triplet energy differences (ΔE_ST) in diradicals. A theory for qualitatively predicting the ground states of diradicals and the use of Negative Ion Photoelectron Spectroscopy (NIPES) for measuring ΔE_ST are described. The application of this theory, ab initio calculations, and NIPES to the prediction and measurement of ΔE_ST in a wide variety of organic diradicals is detailed. Among the diradicals that are discussed in this perspective are HN, CH₃N, PhN, CH₂, trimethylenemethane (TMM), oxyallyl (OXA), meta-benzoquinodimethane (MBQDM), meta-benzoquinone (MBQ), tetramethyleneethane (TME), 1,2,4,5-tetramethylenebenzene (TMB), and D_8h cyclooctatetraene (COT). All of these diradicals have been studied in one and, in most cases, in both of the authors’ laboratories. The studies of OXA and D_8h COT were, in fact, collaborations between the research groups of the authors. These two projects both took advantage of the ability of NIPES to provide information about transition states. Transition-state spectroscopy was used to measure the carbonyl stretching frequency in the singlet state of OXA and to establish that D_8h COT violates the strictest version of Hund's rule.