The catalytic cycle of the oxygen-evolving complex (OEC) of photosystem II (PSII) comprises five intermediate states Si (i = 0–4), from the most reduced S0 state to the most oxidized S4, which spontaneously evolves dioxygen. The precise geometric and electronic structure of the Si states, and hence the mechanism of O–O bond formation in the OEC, remain under investigation, particularly for the final steps of the catalytic cycle. Recent advances in protein crystallography based on X-ray free-electron lasers (XFELs) have produced new structural models for the S3 state, which indicate that two of the oxygen atoms of the inorganic Mn4CaO6 core of the OEC are in very close proximity. This has been interpreted as possible evidence for “early-onset” O–O bond formation in the S3 state, as opposed to the more widely accepted view that the O–O bond is formed in the final state of the cycle, S4. Peroxo or superoxo formation in S3 has received partial support from computational studies. Here, a brief overview is provided of spectroscopic information, recent crystallographic results, and computational models for the S3 state. Emphasis is placed on computational S3 models that involve O–O formation, which are discussed with respect to their agreement with structural information, experimental evidence from various spectroscopic studies, and substrate exchange kinetics. Despite seemingly better agreement with some of the available crystallographic interpretations for the S3 state, models that implicate early-onset O–O bond formation are hard to reconcile with the complete line of experimental evidence, especially with X-ray absorption, X-ray emission, and magnetic resonance spectroscopic observations. Specifically with respect to quantum chemical studies, the inconclusive energetics for the possible isoforms of S3 is an acute problem that is probably beyond the capabilities of standard density functional theory.