Phase-change materials are of intense research interest due mainly to their use in phase-change memory (PCM) devices that are emerging as a promising technology for future non-volatile, solid-state, electrical storage. Electrically driven transitions from the amorphous to the crystalline phase in such devices exhibit characteristic threshold switching. Several alternative electronic explanations for the origins of this characteristic behaviour have been put forward, for example Poole–Frenkel effects, delocalisation of tail states, field emission processes and space charge limited currents [for a full discussion, see Radielli et al., J. Appl. Phys. 103, 111101 (2008) and Simon et al., MRS Proc. 1251, H01–H011 (2010)]. However, an alternative to these conventional electronic models of threshold switching is based on electric field induced lowering of the system free energy, leading to the field induced nucleation of conducting crystal filaments. In this paper we investigate this alternative view. We present a detailed kinetics study of crystallisation in the presence of an electric field for the phase-change material Ge2Sb2Te5. We derive quantitative crystallisation maps to show the effects of both temperature and electric field on crystallisation and we identify field ranges and parameter values where the electric field might play a significant role. Then we carry out physically realistic simulations of the threshold switching process in typical phase-change device structures, both with and without electric field dependent energy contributions to the system free energy. Our results show that threshold switching can be obtained by a mechanism driven purely by electric field induced nucleation, but the fields so required are large, of the order of 300 MV m−1, and significantly larger than the experimentally measured threshold fields.