The growth of a vapour bubble at a heated surface involves various fluid mechanics, heat transfer and phase change phenomena. In this paper we present recent work under the auspices of the NURESAFE project aimed at developing mechanistic modelling of this. Evaporation at the curved surface of the bubble requires evaluation of the unsteady heat conduction within the surrounding liquid, coupled to an appropriate phase change model at the vapour–liquid interface. Issues around the development and implementation of such a phase change model are addressed. For low-pressure bubbles, however, a large fraction of the total evaporation takes place from the “microlayer”; a thin layer of water coating the heated substrate, which is left behind as the bubble expands. This microlayer evaporation requires careful, sub-grid modelling, as heat fluxes through the thin layer are very high. In particular, we demonstrate here the need both for modelling of the conjugate heat transfer within the substrate, and the importance of the incorporation of evaporative thermal resistance at the vapour–liquid interface. Despite the important role it plays in bubble growth, the mechanisms governing the formation, and resulting dimensions, of this microlayer are very little understood. We finish with a presentation of some early results attempting to investigate mechanistically the hydrodynamics of microlayer formation.