We present a review of the spin and statistics of topological geons, particles in3+1quantum gravity. They can have half-odd-integral spin and fermionic statistics and since the underlying gravitational field is tensorial and bosonic, this is an example of “emergent” non-trivial spin and statistics as displayed by familiar non-gravitating objects such as skyrmions. We give the topological background and show that in a “canonical” quantization of gravity there is no spin-statistics correlation for topological geons. Allowing the topology of space to change, for example in a sum-over-histories approach, raises the possibility that a spin-statistics correlation can be recovered for geons. We review a conjectured set of rules powerful enough to give such a spin-statistics correlation for all topological geons. These would appear to rule out the possibility of parastatistics and may rule out spinorial and fermionic geons altogether. ©2000 American Institute of Physics.