Helen Ougham and I recently published an article with this title in a special issue of New Phytologist on Plant developmental evolution. Our paper is a commentary on a very nice study in the journal by Runions et al. in which computational methods were used to generate a wide range of virtual leaf morphologies. This led us to consider the history of ideas about the origins of shape and size in biology and the influence of great thinkers, notably D’arcy Wentworth Thompson, Alan Turing, Michael Faraday, James Clerk Maxwell, Conrad Waddington, Thomas Hunt Morgan and even Plato himself. The central message of the piece is that the generation of leaf form is a deep problem of morphogenesis, requiring the full toolkit of modern evolutionary and developmental biology to break it open.