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, modeling. 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 summarized, and their electrochemical characteristics are related to electrical performance. Given the high interest in system modeling and a large number of papers published on this topic, modeling techniques are classified, explained, and compared, addressing their strengths and weaknesses, and the experimental techniques used to measure the modeled properties are described. Finally, SCs are successfully used in the market sectors, as well as their growth expectations are analyzed. The analysis presented herein gives the account of the expansion that the SC market is currently undergoing and identifies the most promising research trends on this field.