Singlet exciton fission is a carrier multiplication process in organic semiconductors that generates two electron–hole pairs for each photon absorbed. Singlet fission occurs on sub-100 fs timescales with yields of up to 200%, and photovoltaic devices based on singlet fission have achieved external quantum efficiencies above 100%. The major challenge for the field is to use singlet fission to improve the efficiency of conventional inorganic solar cells, such as silicon, and to break the Shockley–Queisser limit on the efficiency of single-junction photovoltaics. Achieving this goal requires a broader and more collaborative effort than the one used at present. Synthetic chemists, spectroscopists, theorists, materials scientists, device physicists and engineers will need to work together. In this Review, we critically assess the current status of the field, highlight the key results and identify the challenges ahead. In doing so, we seek to open the field to new expertise and ideas, which will in turn promote both fundamental science and device applications. Singlet exciton fission is a carrier multiplication process in organic semiconductors that could be used to enhance the efficiency of conventional inorganic solar cells and break the Shockley–Queisser limit of single-junction photovoltaics. In this Review, recent progress in the field is assessed, highlighting the key results and identifying the crucial challenges ahead.