Electrochemical carbon capture and concentration (eCCC) offers a promising alternative to thermochemical processes as it circumvents the limitations of temperature-driven capture and release. This review will begin by discussing the history of eCCC, describing early work in the field and the motivation for pursuing such a process. We will then transition towards discussing more recent approaches, with a heavier emphasis on methods that employ redox mediators to facilitate CO2 capture and release. These methods rely more on optimization through chemical design and include pH-mediated systems, electrochemically-mediated amine regeneration, and direct capture with redox-active molecules. For each approach, we provide a general overview of the system, discuss redox mediator chemistries that have been studied in literature, and highlight requirements for future generations of redox mediators. We also describe previous demonstrations of each method and current cell/system designs that have been used at the lab-scale. To conclude, we summarize achievements in the field, current challenges, and opportunities for improving these technologies. Overall, this review is a comprehensive survey of the eCCC field and evaluates the chemical, theoretical, and electrochemical engineering aspects of this approach. We hope this work can be used to assist the community in the development of modern economical eCCC technologies that can be utilized in large-scale CCS processes.