Small aerosol droplets, ranging in size from 1-10 nm, play a central role in the chemistry and physics of the atmosphere. They affect climate by absorbing and reflecting solar radiation, enhance ice nucleation and act as solvent vessels, or heterogeneous surfaces, for important atmospheric chemical reactions. The physical state of the droplets influence all these processes, but nanoscale systems often exhibit unique phase behaviour and their properties become size dependent. This talk will discuss two nanoscale phase transitions. First, we will examine the nature of the glass transition in nanoparticle systems using molecular dynamics simulation, and compare their thermodynamic and dynamic behaviour with bulk glass forming systems. Second, we will develop a small systems liquid-drop model to describe how systems size effects liquid-liquid phase transitions, and examine how the presence of a liquid-liquid phase transition in the droplets influences condensation from the vapour.