Singlet exciton fission is a carrier multiplication process in organic semiconductors, which allows for the generation of two electron-hole pairs for each photon absorbed. First discovered in the late 1960s, the area has witnessed an explosion of interest within the last 5 years, with demonstrations that singlet fission can occur on sub 100fs timescales, with 200% yield and can be used to build photovoltaics with external quantum efficiencies above 100% percent. The grand challenge of the field is to use singlet fission to enhance the efficiency of conventional inorganic solar cells, such as silicon, and break the Shockley-Queisser limit on the efficiency of single junction photovoltaics. Achieving this goal will require a greatly broadened effort than at present, with collaboration between synthetic chemistry, spectroscopy, theory, material science, organic and inorganic semiconductor device physics and engineering. This review critically assesses the current state of the field, highlighting the key results and identifying the crucial challenges ahead. In doing so, we seek to open the area to new expertise and ideas, which will in turn further both fundamental science and device applications.