Settled and unsettled issues in particle settling

Colloid sedimentation has played a seminal role in the development of statistical physics thanks to the celebrated experiments by Perrin, which provided a concrete demonstration of molecular reality and gave strong support to Einstein's theory of Brownian motion. This review, which mostly focuses on settling at low Peclet number, where Brownian fluctuations are dominant, aims to show that a lot more can be learnt both from the sedimentation equilibrium and from the particle settling dynamics of a wide class of systems, ranging from simple colloids to mesogenic suspensions, from soft solids to active particles and living organisms. At the same time, the occurrence of unexpected and surprising effects brings about challenging questions in statistical and fluid mechanics that make sedimentation an exciting field of research.