Energy storage systems are playing an increasingly important role in a variety of applications, such as electric vehicles or grid-connected systems. In this context, supercapacitors (SCs) are gaining ground due to their high power density, good performance and long maintenance-free lifetime. For this reason, SCs are a hot research topic, and several papers are being published on material engineering, performance characterization, modelling and post-mortem analysis. A compilation of the most important millstones on this topic is essential to keep researchers on related fields updated about new potentials of this technology. This review paper covers recent research aspects and applications of SCs, highlighting the relationship between material properties and electrical characteristics. It begins with an explanation of the energy storage mechanisms and materials used by SCs. Based on these materials, the SCs are classified, their key features are summarised, and their electrochemical characteristics are related to electrical performance. Given the high interest in system modelling and the large number of papers published on this topic, modelling techniques are classified, explained and compared, addressing their strengths and weaknesses, and the experimental techniques used to measure the modelled properties are described. Finally, the market sectors in which SCs are successfully used, as well as their growth expectations are analysed. The analysis presented herein gives account of the expansion that SC market is currently undergoing and identifies the most promising research trends on this field. This work was supported in part by the Spanish State Research Agency (AEI) and FEDER UE under Grant DPI2016-80641-R and Grant DPI2016-80642-R, in part by the Government of Navarre through the Research Project PI020 RENEWABLE-STORAGE, and in part by the FPU Program of the Spanish Ministry of Education, Culture and Sport under Grant FPU13 /00542.