Unified state diagram for the yielding transition. For small amplitude of deformations, soft systems such as mayonnaise or toothpaste present a solid-like dynamics (blue points) with weak fluidity. As the deformation amplitude grows, this class of soft systems undergoes the yielding transition (grey points), characterized by the coexistence between the two types of dynamics (solid and fluid), and finally are fluidified at very large deformations, for which the microscopic dynamics is that of a liquid. (Copyright © 2023, the authors under exclusive license of Springer Nature Limited)