  We present the explicit metric forms for higher dimensional vanishing scalar
invariant (VSI) Lorentzian spacetimes. We note that all of the VSI spacetimes
belong to the higher dimensional Kundt class. We determine all of the VSI
spacetimes which admit a covariantly constant null vector, and we note that in
general in higher dimensions these spacetimes are of Ricci type III and Weyl
type III. The Ricci type N subclass is related to the chiral null models and
includes the relativistic gyratons and the higher dimensional pp-wave
spacetimes. The spacetimes under investigation are of particular interest since
they are solutions of supergravity or superstring theory.
