  This paper reviews recent work on a new geometric object called a bundle
gerbe and discusses some new examples arising in quantum field theory. One
application is to an Atiyah-Patodi-Singer index theory construction of the
bundle of fermionic Fock spaces parametrized by vector potentials in odd space
dimensions and a proof that this leads in a simple manner to the known
Schwinger terms (Mickelsson-Faddeev cocycle) for the gauge group action. This
gives an explicit computation of the Dixmier-Douady class of the associated
bundle gerbe. The method works also in other cases of fermions in external
fields (external gravitational field, for example) provided that the APS
theorem can be applied; however, we have worked out the details only in the
case of vector potentials. Another example, in which the bundle gerbe curvature
plays a role, arises from the WZW model on Riemann surfaces. A further example
is the `existence of string structures' question. We conclude by showing how
global Hamiltonian anomalies fit within this framework.
