How can we explain the fundamental paradox of living matter, which combines stability and robustness of form with constant internal dynamics? It is not only the genetic information contained in every cell, but also numerous stochastic biomolecular processes that are at work in morphogenesis. In addition, the shaping of an organism is driven by mechanical forces that operate within and between cells, across tissues and organs. The dynamics of morphogenesis is a self-organized process that emerges from biological control and physical constraints at all scales. Its study is currently bringing together a fast-growing interdisciplinary community that observes, analyses and models living organisms.