Electric vehicle carsharing (EV-carsharing) systems not only change how people travel, but also provide economic and environmental benefits. However, EV-carsharing systems also create a series of new service operation issues resulting from the characteristics of EVs. From the EV-carsharing system supply side, these issues include an insufficient number of charging stations, high vehicle relocation costs and untimely charge scheduling. From the EV-carsharing system demand side, they include an insufficient understanding of the factors affecting EV-carsharing demand and inaccurate demand forecasts. These issues have hindered the rapid spread of EV-carsharing systems and must be resolved if the development of this industry is to accelerate. We review the most recent EV-carsharing system literature based on different methodologies from the perspectives of supply and demand. According to the research themes, first, we describe the literature on the supply side of EV-carsharing systems as strategic planning (charging station location, number, capacity and fleet size), daily operations (vehicle relocation and vehicle charging) and integrated modelling for strategic planning and daily operations. Optimization models and algorithms are surveyed in each theme. Then, we describe the literature on the demand side of EV-carsharing systems according to the factors affecting EV-carsharing demand and demand forecasting methods. Finally, we propose future research directions for EV-carsharing systems from the perspectives of supply and demand and highlight future research opportunities for EV-carsharing systems given the influence of autonomous driving technologies.