Comprising of earth-abundant, inexpensive, and environmentally friendly elements, kesterite Cu2ZnSn(S,Se)4 (CZTSSe) solar cells are demonstrated to have enormous potential to be an excellent alternative to the commercial Cu(In,Ga)(S,Se)2 (CIGSSe) and CdTe thin-film solar cells. However, the record power conversion efficiency (PCE) of CZTSSe is only 13.0%, which lags far behind state-of-the-art commercial thin-film solar cells (22%-23%). A wide variety of carrier recombination centers, including defects, defect clusters, and secondary phases, which cause nonradiative recombination of carriers and photovoltage loss of the CZTSSe device, is assumed to be the main arch-criminal for poor efficiency. This review focuses on frontier modification strategies to suppress charge recombination. The adverse effects caused by defects and secondary phases in kesterite CZTSSe thin-film solar cells are elucidated. Meanwhile, the recent advances in kesterite CZTSSe solar cells are summarized from extrinsic cation doping, interface engineering, and removal of secondary phases. Finally, the principles of improving the efficiency of CZTSSe are clarified.