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Dispersion management is becoming paramount in high-speed wavelength-division-multiplexed lightwave systems, that operate at per-channel rates of 40 Gb/s and higher. The dispersion tolerances, in these systems, are small enough that sources of dispersion variation, that are negligible in slower systems, become critically important to network performance. At these high-bit rates, active dispersion compensation modules may be required to respond dynamically to changes occurring in the network, such as variations in the per-channel power, reconfigurations of the channel's path that are caused by add-drop operations, and environmental changes, such as changes in ambient temperature. We present a comprehensive discussion of an emerging tunable dispersion compensating device, based on thermally actuated fiber gratings. These per-channel devices rely on a distributed on-fiber thin film heater, deposited onto the outer surface of a fiber Bragg grating. Current flowing through the thin film generates resistive heating at rates that are governed by the thickness profile of the metal film. A chirp in the grating is obtained by using a thin-film, whose thickness varies with position along the length of the grating in a prescribed manner; the chirp rate is adjusted by varying the applied current. The paper reviews some of the basic characteristics of these devices and their implementation, in a range of different applications, including the mitigation of power penalties associated with optical power variations. We present detailed analysis of the impact of group-delay ripple and polarization-mode dispersion on systems performance, and present results from systems experiments, that demonstrate the performance of these devices at bit rates of 10, 20, 40 and 160 Gb/s. We also discuss advantages and disadvantages of this technology, and compare to other devices.