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Adaptive polarization-mode dispersion (PMD) compensation in 10 and 40 Gb/s transmission systems might become necessary if the link PMD causes strong signal distortions, which results in an unacceptable high system outage. The application of PMD compensation has the potential to lead to a drastic improvement of system robustness. Optical and electrical compensators will be reported, their operation principle explained, and their benefits will be quantified. The discussion is focused on the most important structures for practical system application including adaptive feedback loops. Experimental investigations proof compensator concepts which performance conforms with simulations. The electronical feed forward equalizer and the decision feedback equalizer are assessed in comparison to the optical simple and the two-stage compensator and the differences in performance are discussed for statistical PMD limited systems.