jats:secjats:titleAbstract</jats:title>jats:pWe review the materials science applications of the nested sampling (NS) method, which was originally conceived for calculating the evidence in Bayesian inference. We describe how NS can be adapted to sample the potential energy surface (PES) of atomistic systems, providing a straightforward approximation for the partition function and allowing the evaluation of thermodynamic variables at arbitrary temperatures. After an overview of the basic method, we describe a number of extensions, including using variable cells for constant pressure sampling, the semi-grand-canonical approach for multicomponent systems, parallelizing the algorithm, and visualizing the results. We cover the range of materials applications of NS from the past decade, from exploring the PES of Lennard–Jones clusters to that of multicomponent condensed phase systems. We highlight examples how the information gained via NS promotes the understanding of materials properties through a novel way of visualizing the PES, identifying thermodynamically relevant basins, and calculating the entire pressure–temperature(–composition) phase diagram.</jats:p></jats:sec>jats:secjats:titleGraphic abstract</jats:title></jats:sec>