Nested sampling is a general method for Bayesian inference that can produce a sample from the posterior (like MCMC), an estimate of the marginal likelihood (ML) (like stepping stone analyses) as well as an estimate in the variance of the ML (unlike any other practical method) all in a single analysis. This talk will explain the theory and attempts to give some intuition in the workings of nested sampling. We will also look at the practice of nested sampling for phylogenetic inference, how to tune and diagnose problems. Finally, I’ll talk about two variants that look particularly promising — nested importance sampling and dynamic nested sampling — and the progress we made in these last two areas. Nested sampling is implemented as the BEAST 2 package NS.