Our recent analysis of laboratory data, supported by thermodynamic calculations, suggest that pure supercooled droplets of any type of material must freeze or crystallize from the outside in, rather than from the inside out. This conclusion goes against the standard and classical theory of crystallization kinetics, where the phase change process has always been assumed to initiate inside a droplet volume rather than on its surface. The phase change process in two specific systems of atmospheric importance will be discussed, namely the freezing of supercooled water droplets into ice particles and the crystallization of polar stratospheric solution droplets into hydrates of nitric acid. The implications of this finding for atmospheric chemistry and climate research will be discussed.