  A discussion of torsion of Riemannian G-structures leads to a survey of
contributions of Alfred Gray and others on almost Hermitian manifolds,
G_2-manifolds, curvature identities, volume expansions, plotting geodesics, and
the geometry of nilmanifolds. The paper concludes with a new example of a
compact 8-manifold with a quaternionic 4-form that is closed but not parallel.
