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The talk will give an introduction into the X-ray and gamma-ray polarimetry. A particular emphasis will be put onto Compton polarimetry. The application of using segmented germanium detectors for this purpose will be discussed along with an experiment performed at the storage ring ESR in GSI Darmstadt, Germany. This experiment addressed the topic "linear polarization of Radiative Recombination" - the time reversed process of photoionization. Here the relativistic and the retardation effects were found to play an important role, leading to depolarization of the emitted radiation. Different ways of extending the Compton techniques into higher and lower photon energies will be discussed. At the end of the talk other photon polarimetry techniques will be shortly overviewed.