Photovoltaics has become a significant branch of next-generation sustainable energy production. Kesterite Cu2ZnSn(S, Se)4 (copper-zinc-tin-(sulfur, selenium) or CZTS(Se)) is considered one of the most promising, earth-abundant, and nontoxic candidates for solar energy generation over the last decade. However, shallow phase stability of the quaternary phase and the presence of various secondary phases and defects are the main hindrances in achieving the target device performance. This paper summarizes various approaches to synthesize the CZTS absorber layer and the CdS n-type material layer. Besides, different CZTS solar cell device structures, as well as a comprehensive review of secondary phases and defects, have been illustrated and discussed. At last, this review is intended to highlight the current challenges and prospects of CZTS solar cells.