Cu2ZnSn(S,Se)4 is among the most promising inorganic photoabsorbers for thin film solar cells. Characteristics such as a high absorption coefficient, solution-processability, and earth-abundant constituents highlight its potential for large-scale photovoltaics. However, the photovoltaic performance of Cu2ZnSn(S,Se)4 has so far been hindered by open-circuit voltage losses (ΔVOC) in the radiative (ΔVOCRad) and non-radiative limit (ΔVOCNrad), due to sub-bandgap absorption and deep defect states, respectively. Suppressing these two major loss factors could propel Cu2ZnSn(S,Se)4 towards commercial relevance. In the past 2 years, record efficiency approaching 15% has been reported, prompting a renewed interest that the performance-limiting factors have been overcome. In this perspective, we quantify the ΔVOC for the recently reported high power conversion efficiency devices, compare the relevant photovoltaic metrics to previous records, and offer directions for future research. We find that ΔVOCRad due to bandgap fluctuations and Urbach tails has been suppressed in the recent record devices, with values approaching those for record efficiency Cu(In,Ga)(S,Se)2 solar cells. However, we also find that the recombination parameter J0, which more closely relates to the ΔVOCNrad, only shows modest improvements compared to previous records, and has values that must be improved by about four to six orders of magnitude to compete with those for Cu(In,Ga)(S,Se)2 solar cells. The impressive performance gains that have been achieved by suppressing ΔVOCRad must now be built upon to suppress ΔVOCNrad. Our analysis points out that the next level of breakthrough in power conversion efficiency will be achieved by reducing the non-radiative recombination due to deep defects in the bulk, and at grain boundaries and interfaces.