Despite the numerous studies on heat pipes over the last fifty years, the development of predictive tools for the design of heat pipes remains challenging, even for conventional technologies. As a result, heat pipes are still the object of more than 250 scientific articles a year. The present review aims to identify and understand the current scientific approaches followed by scientists in heat pipe science. The different types of heat pipe are reviewed in order to identify the main phenomena involved in these systems. A brief overview of the heat pipe history is given and the different applications are presented. A global review of the recent studies on heat pipes is then presented. Advances are identified in terms of heat pipe characterisation, scientific issues linked to the working fluid, understanding of phase-change heat transfer in thin liquid films and system modelling. Examples of recent works are detailed to highlight the strategies that can be followed to answer the current issues. This global review enables to highlight the main advances on heat pipe science of the last five years and to draw perspectives on the forthcoming scientific results.