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This article discusses the creation of adaptive algorithms for channel shortening, with particular attention to blind algorithms. The context is multicarrier modulation, through other applications of channel shortening are discussed. It is shown that the algorithms used for adaptive equalization are not easily applied to adaptive channel shortening. In a return to first principles, a property restoral design philosophy is put forth and several recent property-restoral-based approaches to adaptive channel shortening are reviewed. The authors conclude with a discussion of the limitations of the current approaches and a list of open problems in the area of adaptive channel shortening.