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The complex interplay of processes that govern the size, composition, phase and morphology of aerosol particles in the atmosphere is challenging to understand and model. Measurements on single aerosol particles (2 to 100 mm in diameter) held in electrodynamic, optical and acoustic traps or deposited on a surface can allow the individual processes to be studied in isolation under controlled laboratory conditions. In particular, measurements can now be made of particle size with unprecedented accuracy (sub-nanometre) and over a wide range of timescales (spanning from milliseconds to many days). The physical state of a particle can be unambiguously identified and its composition and phase can be resolved with a high degree of spatial resolution. In this review, we describe the advances made in our understanding of aerosol properties and processes from measurements made of phase behaviour, hygroscopic growth, morphology, vapour pressure and the kinetics of water transport for single particles. We also show that studies of the oxidative aging of single particles, although limited in number, can allow the interplay of these properties to be investigated. We conclude by considering the contributions that single particle measurements can continue to make to our understanding of the properties and processes occurring in atmospheric aerosol.