Solar energy is one of the renewable energies being researched extensively owing to the scarcity of fossil fuels, besides the global concern on climate change. Consequently, intensive research activities have been conducting on solar cell material technology. Chalcopyrites (i.e., CIS, CISe, CIGS and CZTS) are suitable candidates for future improvement of solar cell technology as they provide a low-cost alternative to Si thin-film solar cells. Amongst the chalcopyrite family, copper indium gallium diselenide (CIGS) is considered to be a leading thin-film solar cell material. In this paper, a review of the electrodeposition process as a fabricating method for CIGS thin-film solar cells has been presented. The potential challenges encountered while depositing the absorber layers, and the effects of adding complexing agents to overcome such encountered challenges have been discussed. Moreover, past and record efficiencies, in addition to state-of-the-art research in the areas of finding alternative possibilities to overcome the issues with the selenization step as well as suitable solutions to deal with the issues associated with gallium incorporation have been reviewed. Future probable solutions have also been provided to these challenges. In short, this review brings together all the aspects related to CIGS solar cells to enrich the field and support the interested industry and researchers.