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In this paper we describe the design of different X-ray Talbot interferometers that have been built at the tomography beamline ID19 of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, and give a short review of performance characteristics, of current developments, and of the results obtained with these instruments so far. Among the applications so far, soft-tissue imaging has been a particular focus, as demonstrated in a recent paper by Schulz et al. (J. Roy. Soc. Interface, in press).