  We survey briefly the definition of the Rozansky-Witten invariants, and
review their relevance to the study of compact hyperkahler manifolds. We
consider how various generalisations of the invariants might prove useful for
the study of non-compact hyperkahler manifolds, of quaternionic-Kahler
manifolds, and of relations between hyperkahler manifolds and Lie algebras. The
paper concludes with a list of additional problems.
