Marginal ice zones (MIZs) are qualitatively distinct sea-ice-covered areas that play a critical role in the interaction between the polar oceans and the broader Earth system. MIZ regions have high spatial and temporal variability in oceanic, atmospheric and ecological conditions. The salient qualitative feature of MIZs is their composition as a mosaic of individual floes that range in horizontal extent from centimetres to tens of kilometres. Thus the floe size distribution (FSD) can be used to quantitatively identify and describe them. Here, the history of FSD observations and theory, and the processes (particularly the impact of ocean waves) that determine floe sizes and size distribution, are reviewed. Coupled wave-FSD feedbacks are explored using a stochastic model for thermodynamic wave-sea-ice interactions in the MIZ, and some of the key open questions in this rapidly growing field are discussed. This article is part of the theme issue 'Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks'.
Keywords: ocean surface waves; polar climate; sea ice.