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Foldable solar cells, with the advantages of size compactness and shape transformation, have promising applications as power sources in wearable and portable electronics, building and vehicle integrated photovoltaics. However, in contrast to mild bending with curvature radius of several millimeters, folding generates the crease with extreme curvature radius of sub-millimeter, resulting in the appearance of large strain and stress. As a result, it is highly challenging to realize robustly foldable and highly efficient solar cells. Here, we summarize the recent progress on photovoltaic performance and mechanical robustness of foldable solar cells. The key requirements to construct highly foldable solar cells, including structure design based on turning the neutral axis plane, and adopting flexible alternatives including substrates, transparent electrodes and absorbers, are intensively discussed. In the end, some perspectives for the future development of foldable solar cells, especially the standard folding procedure, improvement in the folding endurance through revealing failure mechanisms, are provided.