Carbon capture and storage (CCS) is a technology enabling to use fossil fuels in a sustainable way. Therefore, it attracts much attention from the industrial sector, government authorities and scientific community. However, public awareness of the technology is extremely low, and the studies of the lay people's opinion have been launched only during the last decade. Taking into account the role of public support during the implementation of CCS projects, the authors would like to present herein their review of materials on this subject published during 2002–2018 (135 articles). As part of our review, we determined 9 key aspects forming the public perception of CCS. For each of the key aspects, we summarized the available results of the studies. Apart from that, we compared the CCS current status in different countries and provided a number of reasons for involving new countries into the fight against global warming. This work shows that most attention is devoted to CO2 storage; whereas its capture and transportation are poorly studied in terms of public perception. Wider development is required for the methodology enabling a transition from global rhetoric concerning global warming issues to the implementation of particular projects, namely, CCS. The issues related to public awareness of CCS are studied rather thoroughly, but no recommendations are provided regarding the establishment of an optimal database for the lay people. Numerous assessments of general public perception have been carried out. However little attention was paid to the regions with active projects, namely, to the factors considered the most important by the local public, and how actual project results meet their expectations. Therefore, despite an extensive scientific base developed over 17 years, further studies should be aimed at filling the existing gaps. This will enable to improve CCS attractiveness for the public, including the cases when it is compared with alternative low-carbon technologies.