Nested sampling for physical scientists

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms practice high-dimensions, including methods from so-called constrained prior. outline ways which may be applied describe application three scientific fields has proved to useful: cosmology, gravitational-wave astronomy, materials science. close by making recommendations best when using summarizing potential limitations optimizations NS.