We discuss recent work on reaction-diffusion processes that take place on complex networks. The inherent inhomogeneity of the substrate leads to a series of new phenomena, which bear only a small resemblance to the classical results of the field. The annihilation rate is abnormally high in such systems, while at the same time depletion zones are absent in the A + A -> 0 reaction and no segregation is observed for the A + B -> 0 reaction. These results are mainly attributed to the presence of network hubs and to the small network diameter of such systems.
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