Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate N−1/2, where N is a tuning parameter proportional to the computational effort, and that this error is asymptotically Gaussian.We show that the asymptotic variance of the nested sampling approximation typically grows linearly with the dimension of the parameter. We discuss the applicability and efficiency of nested sampling in realistic problems, and we compare it with two current methods for computing marginal likelihood. We propose an extension that makes it possible to avoid resorting to MCMC to obtain the simulated points.