  We describe a topological effect on configurations of D-branes in the
presence of NS-NS and RR field strength fluxes. The fluxes induce the
appearance of chiral anomalies on lower dimensional submanifolds of the D-brane
worldvolume. This anomaly is not associated to a dynamical chiral fermion
degree of freedom, but rather should be regarded as an explicit flux-induced
anomalous term (Wess-Zumino term) in the action. The anomaly is cancelled by an
inflow mechanism, which exploits the fact that fluxes can act as sources of RR
fields. We discuss several applications of this flux-induced anomaly; among
others, its role in understanding anomaly cancellation in compactifications
with D-branes and fluxes, and the possibility of phase transitions where a
chiral fermion disappears from the D-brane world-volume spectrum, being
replaced by an explicit Wess-Zumino term. We comment on the relation among
different mechanisms to obtain four-dimensional chirality in string theory.
