Morphogenesis is the remarkable process by which a developing organism acquires its shape. As morphogenesis entails dynamic changes in the structural elements that define shape, it is essential to investigate the role of the mechanical properties of these elements in an organismal context. Does cell differentiation lead to modifications in mechanical properties? Do these mechanical properties predict shape changes? More generally, what are the principles behind morphogenesis? In this talk, I will present some of our approaches to tackle these questions, focussing on growth dynamics at the tip of plant shoots and in leaves. A number of studies have shown that growing thin sheets undergo buckling and wrinkling by default. In particular, we found that when growth is enhanced near the edge, the equilibrium configuration of the sheet is fractal-like, accounting for the shape of beet or lettuce leaves. This default, wrinkled state raises the question of how a flat shape is maintained, and implies the existence of mechanisms that regulate growth in plant tissues. We investigated such a mechanism using a combination of biological and physical approaches. This led us to counter-intuitive results on stochasticity in plant morphogenesis.