Abstract: Within Berger?s classification of holonomy groups, G? is the distinguished case in dimension seven, and a G?-holonomy metric determines a parallel 3-form. As in other special geometries, the existence of such metrics imposes topological constraints on compact manifolds; analogues in Kähler geometry include the hard Lefschetz property, the Hodge decomposition, and formality. Formality, first discovered as a property of compact Kähler manifolds by Deligne, Griffiths, Morgan, and Sullivan in 1975, depends on the rational homotopy type of a manifold. Subsequent results lead to the conjecture that special and exceptional holonomy manifolds should be formal. In this talk, we discuss the only counterexample known to date: a compact holonomy G? manifold that is not formal.