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Polymeric substrates are being identified that could permit translation of human pluripotent stem cells from laboratory-based research to industrial-scale biomedicine. Well-defined materials are required to allow cell banking and to provide the raw material for reproducible differentiation into lineages for large-scale drug-screening programs and clinical use. Yet more than 1 billion cells for each patient are needed to replace losses during heart attack, multiple sclerosis and diabetes. Producing this number of cells is challenging, and a rethink of the current predominant cell-derived substrates is needed to provide technology that can be scaled to meet the needs of millions of patients a year. In this Review, we consider the role of materials discovery, an emerging area of materials chemistry that is in large part driven by the challenges posed by biologists to materials scientists.