The structure of γ-Al2O3, the most important catalyst support, is still under discussion; especially the positions of the Al3+cations and vacancies are debated. One model proposes that γ-Al2O3 consists of irregularly stacked nanocrystals with all Al3+ cations occupying spinel positions, another that some Al3+ cations occupy non-spinel positions, while a third model proposes that γ-Al2O3 does not have a spinel structure. 17O and 27Al NMR measurements showed that 62.5–65% of the cations are at octahedral positions, in agreement with a spinel structure model, with DFT calculations, and with isostructural γ-Fe2O3, but in disagreement with the non-spinel model. A reconsideration of the non-spinel model is, therefore, strongly recommended. In agreement with DFT calculations, TEM measurements showed that strong reconstruction of the surface of γ-Al2O3 occurs. The (1 1 0) surface of γ-Al2O3 is not atomically flat but forms nanoscale (1 1 1) facets, indicating that (1 0 0) and (1 1 1) facets have the lowest energy.