All photovoltaic solar cells transmit photons with energies below the absorption threshold (bandgap) of the absorber material, which are therefore usually lost for the purpose of solar energy conversion. Upconversion (UC) devices can harvest this unused sub-threshold light behind the solar cell, and create one higher energy photon out of (at least) two transmitted photons. This higher energy photon is radiated back towards the solar cell, thus expanding the utilization of the solar spectrum. Key requirements for UC units are a broad absorption and high UC quantum yield under low-intensity incoherent illumination, as relevant to solar energy conversion devices, as well as long term photostability. Upconversion by triplet-triplet annihilation (TTA) in organic chromophores has proven to fulfil the first two basic requirements, and first proof-of-concept applications in photovoltaic conversion as well as photo(electro)chemical energy storage have been demonstrated. Here we review the basic concept of TTA-UC and its application in the field of solar energy harvesting, and assess the challenges and prospects for its large-scale application, including the long term photostablity of TTA upconversion materials.