  Rozansky and Witten proposed in 1996 a family of new three-dimensional
topological quantum field theories, indexed by compact (or asymptotically flat)
hyperkaehler manifolds. As a byproduct they proved that hyperkaehler manifolds
also give rise to Vassiliev weight systems. These may be thought of as
invariants of hyperkaehler manifolds, so the theory is of interest to geometers
as well as to low-dimensional topologists. This paper surveys the geometrical
construction of the weight systems, how they may be integrated into the
framework of Lie algebra weight systems (joint work with Simon Willerton),
their applications, and an approach to a rigorous construction of the TQFTs
(joint work with Justin Sawon and Simon Willerton).
