  Spacetimes in which the electric part of the Weyl tensor vanishes (relative
to some timelike unit vector field) are said to be purely magnetic. Examples of
purely magnetic spacetimes are known and are relatively easy to construct, if
no restrictions are placed on the energy-momentum tensor. However it has long
been conjectured that purely magnetic vacuum spacetimes (with or without a
cosmological constant) do not exist. The history of this conjecture is reviewed
and some advances made in the last year are described briefly. A generalisation
of this conjecture first suggested for type D vacuum spacetimes by Ferrando and
Saez is stated and proved in a number of special cases. Finally an approach to
a general proof of the conjecture is described using the Newman-Penrose
formalism based on a canonical null tetrad of the Weyl tensor.
