In addition to being crucial to the establishment of archaeological chronologies, radiocarbon dating is vital to the establishment of time lines for many Holocene and late Pleistocene palaeoclimatic studies and palaeoenvironmental reconstructions. The calibration curves necessary to map radiocarbon to calendar ages were originally estimated using only measurements on known age tree-rings. More recently, however, the types of records available for calibration have diversified and a large group of scientists (known as the IntCal Working Group---IWG) with a wide range of backgrounds has come together to create internationally-agreed estimates of the calibration curves. In 2002, Caitlin Buck was recruited to the IWG and asked to offer advice on statistical methods for curve construction. In collaboration with Paul Blackwell, she devised a tailor-made Bayesian curve estimation method which was adopted by the IWG for making all of the 2004 internationally-agreed radiocarbon calibration curve estimates. This paper reports on that work and on the on-going work that will eventually provide models, methods and software for rolling updates to the curve estimates.