Heat pipes and thermosyphons - devices of high effective thermal conductivity - have been studied for many years for enhancing the performance of solid, liquid and phase change material (PCM) heat stores. However, as the applications of heat storage widen, from micro-electronics thermal control to concentrated solar heat storage and vehicle thermal management, and even for chemical reactor isothermalisation, the challenges facing heat storage increasingly are moving from those associated with the 'standard' diurnal storage, in itself a problem for low thermal conductivity materials, to response times measured in a few hours or even minutes. While high thermal conductivity metals such as foams can be impregnated with a PCM, for example, to increase local conductivity, the rapid heat input and removal necessitates a more radical approach - heat pipes, possibly with feedback control, with innovative PCM interfaces. This paper reviews the use of heat pipes in conventional and rapid response thermal storage applications and introduces some novel concepts that might overcome current limitations.