Quaternary semiconducting materials based on the kesterite (A 2 BCX 4) mineral structure are the most promising candidates to overtake the current generation of light-absorbing materials for thin-film solar cells. Cu 2 ZnSnS 4 (CZTS), Cu 2 ZnSnSe 4 (CZTSe) and their alloy Cu 2 ZnSn(Se,S) 4 consist of abundant, low-cost and non-toxic elements, unlike current CdTe and Cu(In,Ga)Se 2 based technologies. Zinc-blende related structures are formed by quaternary compounds, but the complexity associated with the multi-component system introduces difficulties in material growth, characterization, and application. First-principles electronic structure simulations, performed over the past five years, that address the structural, electronic, and defect properties of this family of compounds are reviewed. Initial predictions of the bandgaps and crystal structures have recently been verified experimentally. The calculations highlight the role of atomic disorder on the cation sub-lattice, as well as phase separation of Cu 2 ZnSnS 4 into ZnS and CuSnS 3, on the material performance for light-to-electricity conversion in photovoltaic devices. Finally, the current grand challenges for materials modeling of thin-film solar cells are highlighted.