Despite its widespread use, the composition and structure of gamma-alumina have been the subject of controversy for decades. In this article we review the historical attempts to resolve two principal questions that have each been extensively debated, but in independent communities: (1) What is the distribution of vacancies over the two cation sublattices in the nominal spinel structure, and (2) what is the hydrogen content of gamma-alumina, if any? We then review how recent investigations have shown that these two questions are, in fact, related, and have a single resolution. The experimental study of gamma-alumina surfaces has long been dominated by IR spectroscopy of the hydroxylated surfaces, and Al-27 NMR. Both techniques have produced perplexing results. Here we review the development of these surface studies and parallel computational studies. Finally, we review recent computational results that explain the puzzling experimental findings.