Generalisations of Rozansky-Witten invariants

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.