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Traffic grooming refers to techniques used to combine low-speed traffic streams onto high-speed wavelengths in order to minimize the networkwide cost in terms of line terminating equipment and/or electronic switching. Such techniques become increasingly important for emerging network technologies, including SONET/WDM rings and MPLS/MPλS backbones, for which traffic grooming is essential. In this article we formally define the traffic grooming problem, and we provide a general formulation that captures the features of a wide range of problem variants. We then present a comprehensive comparative survey of the literature that unveils the significant amount of research on this subject (the traffic grooming past). We also offer a broad set of ambitious research directions (the traffic grooming future) that are motivated by the exciting new challenges arising with the advent of MPλS technology.