Tungsten has been recently chosen as the divertor material in ITER and is a leading candidate for use in DEMO and future fusion reactors. Linear plasma device and laboratory experiments have shown substantial nanostructured surface modification in tungsten, of low-density ‘fuzz’-like appearance, when exposed to helium ions with impact energies that are below the displacement damage and sputtering thresholds for tungsten, and under temperature and ion flux conditions likely to be encountered in such fusion devices. Such surface features affect a number of material surface properties, such as heat transfer, embrittlement, and deuterium/tritium retention, and can increase the likelihood of high-Z contamination of the fusion plasma by dust formation. Despite its potential detrimental effects on fusion plasmas, and extensive experimental and theoretical research effort, a complete and comprehensive understanding of fuzz formation is not yet in hand. In this topical review article, the current status of experiment and theory are presented, and some of the remaining issues and open questions discussed.