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Astrometry.net is a reliable and robust system that takes as input an astronomical image and returns as output the pointing, scale, and orientation of that image (the astrometric calibration or World Coordinate System information). The system requires no first guess, and works with the information in the image pixels alone; that is, the problem is a generalization of the "lost in space" problem in which nothing—not even the image scale—is known. After robust source detection is performed in the input image, asterisms (sets of four or five stars) are geometrically hashed and compared to pre-indexed hashes to generate hypotheses about the astrometric calibration. A hypothesis is only accepted as true if it passes a Bayesian decision theory test against a null hypothesis. With indices built from the USNO-B catalog and designed for uniformity of coverage and redundancy, the success rate is >99.9% for contemporary near-ultraviolet and visual imaging survey data, with no false positives. The failure rate is consistent with the incompleteness of the USNO-B catalog; augmentation with indices built from the Two Micron All Sky Survey catalog brings the completeness to 100% with no false positives. We are using this system to generate consistent and standards-compliant meta-data for digital and digitized imaging from plate repositories, automated observatories, individual scientific investigators, and hobbyists.