An assessment is made of the credibility of the radiocarbon dating of the shroud of Turin. The quoted final results produced a calibrated calendar age range of AD 1260–1390 for the linen of the Turin shroud at a 95% confidence level. The measurements were carried out independently in three accelerator mass spectrometry (AMS) laboratories located at the University of Arizona, Tucson, Arizona, USA, Oxford University, Oxford, England, and ETH-Hönggerberg, Zürich, Switzerland with assistance for certification and data analysis provided by the British Museum. The author concludes that, although the procedures followed differed substantially from those recommended at a workshop organized by the Pontifical Academy of Sciences, the results are credible. Although of negligible scientific value, they represent a major public triumph for the AMS method of carbon dating. However, many doubts have been raised, both real and fanciful, concerning the validity of the results and these are discussed. It is suggested that steps should be taken to conserve the shroud and that permission should be given for its examination by experts in medieval art.