In 1949, Willard Libby proposed carbon dating, a method for dating carbon-containing objects (like wood, leather, or cloth) that exploits the radioactive decay of carbon-14. The diagram above [redrawn from J. R. Arnold & W. F. Libby, “Age Determinations by Radiocarbon Content: Checks with Samples of Known Age,” Science 110 (2869), 678–680, 23 Dec 1949] shows the decay curve for carbon-14, together with some comparison samples Libby used (including wood dated by tree rings and items from the tomb of Pharaoh Zoser, for whom the first of the pyramids was built). It’s a very good fit! Later tests of carbon-dating have used dendrochronology back to about 10,000 BC.
The carbon in plants contains about one part per trillion of carbon-14, which the plants absorb from the atmosphere. The same amount of carbon-14 is present in animals, which get their carbon by eating plants or other animals. All living things therefore contain about one part per trillion of carbon-14. In dead plants or animals, however, the carbon-14 decays with a half-life of 5,730 years. For practical dating purposes, measurements of carbon-14 are adjusted to match the tree-ring data, so as to compensate for small changes in the amount of atmospheric carbon-14 over time. Such calibrated dates are reported as “Before Present” (BP), where “Present” means 1 January 1950.
One of the most famous examples of carbon-dating has been the Shroud of Turin, purported to be the burial shroud of Jesus Christ, and shown below in a negative image from 1898. The Shroud has been carbon-dated to between 1260 and 1390 AD, which is consistent with its denunciation as a forgery by the Bishop of Troyes in 1389, shortly after it first appeared on the historical scene. For the dating story, see P. E. Damon et al., “Radiocarbon Dating of the Shroud of Turin,” Nature 337 (6208), 611–615, 16 Feb 1989.