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In simple wavelength-division multiplexed (WDM) networks, a connection must be established along a route using a common wavelength on all of the links along the route. This constraint may be removed by the introduction of wavelength converters, which are devices which take the data modulated on an input wavelength and transfer it to a different output wavelength. Wavelength converters thus improve network blocking performance. However, the introduction of wavelength converters into WDM cross-connects increases the hardware cost and complexity. Thus, it is important to establish precisely what advantages wavelength converters offer WDM networks. There has been considerable interest in the literature in the performance improvements offered by the introduction of wavelength converters into dynamically-reconfigurable WDM networks. This article provides a review of the conclusions drawn from these investigations. The performance improvements offered by wavelength converters depend on a number of factors, including network topology and size, the number of wavelengths, and the routing and wavelength assignment algorithms used. We discuss these factors here. However, it has been shown that wavelength converters offer only modest performance improvements in many networks. We also consider networks with limited wavelength conversion, in which the set of allowable conversions at a network node is constrained by having limited numbers of wavelength converters, or by using non-ideal wavelength converters. Limited wavelength conversion has been shown to provide performance which is often close to that achieved with ideal wavelength conversion in networks with tunable transmitters and receivers.