Some people are of the steadfast belief that the shroud represents the burial cloth of Jesus of Nazareth, the founder of the Christian church; but all radiocarbon dates and scientific testing to date have returned medieval dates. The theory of most scientists and historians is that the shroud was created by an artist in the 14th century using a model who was coated in a combination of red ochre and vermilion, a paint combination commonly used in the middle ages. Whether the original intention was a work of secular art, a hoax meant to fool people, or a thoughtful religious relic made by a follower of Jesus, isn't really available to us today.
The discovery that all five radiocarbon dates were in the 14th century was a setback for those who believe in its direct association with Jesus; and some have argued that the dates were affected by a fire which added carbon monoxide to the fabric. John Jackson, director of the Turin Shroud Center of Colorado and the University of Oxford Radiocarbon Accelerator Unit conducted additional work in an attempt to identify if carbon monoxide might have been a factor in the dates. What they did was experimental archaeology--Dr. Jackson's center subjected modern linen cloth to very high levels of carbon monoxide; and the ORAU monitored the effects.
The results--that exposure to even the highest carbon monoxide levels does not affect modern linen at all--were communicated in a BBC2 documentary this past week.
For more information, see the Oxford Radiocarbon Accelerator Unit webpage.