The treatment of diabetes mellitus represents one of the greatest medical challenges of our era. Diabetes results from a deficiency or functional impairment of insulin-producing β cells, alone or in combination with insulin resistance. It logically follows that the replacement or regeneration of β cells should reverse the progression of diabetes and, indeed, this seems to be the case in humans and rodents. This concept has prompted attempts in many laboratories to create new human β cells using stem-cell strategies to transdifferentiate or reprogramme non-β cells into β cells or to discover small molecules or other compounds that can induce proliferation of human β cells. This latter approach has shown promise, but has also proven particularly challenging to implement. In this Review, we discuss the physiology of normal human β-cell replication, the molecular mechanisms that regulate the cell cycle in human β cells, the upstream intracellular signalling pathways that connect them to cell surface receptors on β cells, the epigenetic mechanisms that control human β-cell proliferation and unbiased approaches for discovering novel molecules that can drive human β-cell proliferation. Finally, we discuss the potential and challenges of implementing strategies that replace or regenerate β cells.