Over the last two decades there has been an accumulation of exciting evidence that appears to show that, as early as 5000 years ago, people in Britain were making precise observations of the Sun, Moon, and stars, and studying small perturbations in the lunar motion. Structures such as Stonehenge, and the s thousands of other megalithic sites in Britain, are then seen as prehistoric observations. Within these, data would be (accumulated to enable the prediction of celestial phenomena such as eclipses, and allow the construction of a calendar. Recently however a small number of rigorous statistical studies of the sites have cast doubt on the astronomical hypotheses, and have posed the question of whether some of the support for these hypotheses has been generated by well-intentioned but over-enthusiastic selections of chance alignments. In this review, the arguments and counter arguments are presented and examined, and we see what can be salvaged from the astronomical hypotheses after the statistical smoke has cleared.