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`Acoustic black holes' are relatively new physical objects that have been introduced and investigated mainly during the last decade. They can absorb almost 100% of the incident wave energy, which makes them attractive for such traditional engineering applications as vibration damping and sound absorption. They could be useful also for some ultrasonic devices using Lamb waves to provide anechoic termination. So far, acoustic black holes have been investigated mainly for flexural waves in thin plates for which the required gradual changes in local wave velocity with distance can be easily achieved by changing the plate local thickness. The present paper provides a brief review of the theory of acoustic black holes, including their comparison with `optic black holes' introduced about three years ago. Review is also given of the recent experimental work carried out at Loughborough University on damping structural vibrations using the acoustic black hole effect. This is followed by the discussion on potential applications of the acoustic black hole effect for sound absorption in air.