Thin-film solar cells based on kesterite solar absorbers have all the potential to play a major role in photovoltaics, but their efficiency needs to be improved further to meet the industry's requirements. Several attempts are made toward improving the absorber quality to surpass the current record efficiency of 13.6%. Doping with isoelectronic, alkali, and other elements has been shown to advance the device performance of thin-film kesterite solar cells as compared to the undoped references. This review gives a summary of such attempts with a focus on solution-processing techniques for extrinsic doping. The discussion on the importance of doping, the different doping elements explored, the merits as well as demerits of the solution-processed technique, and the future prospects is included.