  Supersymmetric solutions of supergravity theories, and consequently metrics
with special holonomy, have played an important role in the development of
string theory. We describe how a Lorentzian manifold is either completely
reducible, and thus essentially known, or not completely reducible so that
there exists a degenerate holonomy invariant lightlike subspace and
consequently admits a covariantly constant or a recurrent null vector and
belongs to the higher-dimensional Kundt class of spacetimes. These Kundt
spacetimes (which contain the vanishing and constant curvature invariant
spacetimes as special cases) are genuinely Lorentzian and have a number of
interesting and unusual properties, which may lead to novel and fundamental
physics.
