The kesterite-structured semiconductors Cu2ZnSnS4 and Cu2ZnSnSe4 are drawing considerable attention recently as the active layers in earth-abundant low-cost thin-film solar cells. The additional number of elements in these quaternary compounds, relative to binary and ternary semiconductors, results in increased flexibility in the material properties. Conversely, a large variety of intrinsic lattice defects can also be formed, which have important influence on their optical and electrical properties, and hence their photovoltaic performance. Experimental identification of these defects is currently limited due to poor sample quality. Here recent theoretical research on defect formation and ionization in kesterite materials is reviewed based on new systematic calculations, and compared with the better studied chalcopyrite materials CuGaSe2 and CuInSe2. Four features are revealed and highlighted: (i) the strong phase-competition between the kesterites and the coexisting secondary compounds; (ii) the intrinsic p-type conductivity determined by the high population of acceptor CuZn antisites and Cu vacancies, and their dependence on the Cu/(Zn+Sn) and Zn/Sn ratio; (iii) the role of charge-compensated defect clusters such as [2CuZn+SnZn], [VCu+ZnCu] and [ZnSn+2ZnCu] and their contribution to non-stoichiometry; (iv) the electron-trapping effect of the abundant [2CuZn+SnZn] clusters, especially in Cu2ZnSnS4. The calculated properties explain the experimental observation that Cu poor and Zn rich conditions (Cu/(Zn+Sn) approximate to 0.8 and Zn/Sn approximate to 1.2) result in the highest solar cell efficiency, as well as suggesting an efficiency limitation in Cu2ZnSn(S,Se)4 cells when the S composition is high.