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Free superfluid helium droplets constitute a versatile medium for a diverse range of experiments in physics and chemistry that extend from studies of the fundamental laws of superfluid motion to the synthesis of novel nanomaterials. In particular, the emergence of quantum vortices in rotating helium droplets is one of the most dramatic hallmarks of superfluidity and gives detailed access to the wave function describing the quantum liquid. This review provides an introduction to quantum vorticity in helium droplets, followed by a historical account of experiments on vortex visualization in bulk superfluid helium and a more detailed discussion of recent advances in the study of the rotational motion of isolated, nano- to micrometer-scale superfluid helium droplets. Ultrafast X-ray and extreme ultraviolet scattering techniques enabled by X-ray free-electron lasers and high-order harmonic generation in particular have facilitated the in situ detection of droplet shapes and the imaging of vortex structures inside individual, isolated droplets. New applications of helium droplets ranging from studies of quantum phase separations to mechanisms of low-temperature aggregation are discussed. 

This chapter aims to look at the properties of large helium nanodroplets from two different perspectives: a.) helium droplets as hosts for assembling and studying clusters at low temperatures; and b.) helium droplets as systems to be studied on their own. First, the thermodynamics and excitations in large droplets are presented, followed by a primer on the droplets’ rate of cooling in vacuum. The chapter then proceeds with the description on producing and characterising the droplets. This subject is followed by a discussion on the kinetics for different regimes of cluster aggregation, such as that for single- and multiple-centre aggregation. Then, experiments involving the spectroscopy of the foreign particles and the deposition of metallic clusters for electron microscopy studies are described. Finally, results from recent x-ray coherent diffractive imaging experiments with pure and doped helium nanodroplets are summarised.