Kekulé first suggested a hexagonal structure for benzene in 1865. For over a half-century after, chemists struggled to reconcile proposed structures for benzene and other aromatic compounds with their resistance to chemical transformation and tendency to maintain the type during reaction. The combined structural and reactivity features of these compounds were eventually covered by the term 'aromaticity'. Kekulé, Bamberger and Thiele had each proposed a criterion for aromaticity; all were either empirically contradicted or incapable of evaluation. In the 1930s, two rival quantum mechanical methods succeeded in establishing a physical basis for aromaticity. Using valence bond theory, Pauling attributed benzene's stability to its being a resonance hybrid of several Lewis structures. Calculating resonance energies was challenging but manipulating Lewis structures was not; that procedure provided qualitative insights into aromatic structure and reactivity. Resonance theory appealed especially to organic chemists and eclipsed Hückel's contemporaneous molecular orbital approach, which remained relatively inaccessible. In the 1950s, however, simple rules derived from Hückel's mathematics, combined with proton NMR data, provided seemingly universal criteria for aromaticity. In the event, post-1950 discoveries of non-organic, three-dimensional compounds such as ferrocene and the fullerenes that exhibit aromatic properties led chemists to doubt the utility and universality of 'aromaticity' as a concept. A recent consensus maintains that aromaticity is a multi-variable phenomenon that cannot be reduced to a strict definition, a property it shares with other core chemical concepts such as 'acidity' and 'reactivity'.