Growth, motion, morphogenesis, and self-organization are features common to all biological systems. Harnessing chemical energy allows biological cells to function out of thermodynamic equilibrium and to alter their number, size, shape, and location. For example, the zygote that results when a mammalian egg and sperm cell fuse divides to form a ball of cells, the blastocyst. Collective cell migrations and remodeling then drive the tissue folding that determines how cells are positioned before they differentiate to grow into the stunning diversity of different living creatures. The development of organoids and tumors is controlled by the confining properties of the viscous, extracellular matrix that surrounds tissues; wounds heal through the collective motion of cell layers and escape from a surface layer into the third dimension, which determines the growth of biofilms. The relevance of stresses, forces, and flows in these processes is clear and forms the basis of the interdisciplinary science of mechanobiology, which draws on knowledge from physics, engineering, and biochemistry to ask how cells organize their internal components, how they move, grow and divide, and how they interact mechanically with each other and with their surroundings. This approach to biological processes is particularly timely, both because of experimental advances exploiting soft lithography and enhanced imaging techniques, and because of progress in the theories of active matter, which is leading to new ways to describe the collective dynamical behavior of systems out of thermodynamic equilibrium. Identifying stresses, forces, and flows, and describing how they act, may be key to unifying research on the underlying molecular mechanisms and to interpreting a wealth of disparate data to understand biological self-organization from molecular to tissue scales.