  Concentrated colloidal suspensions and emulsions are amorphous soft solids,
widespread in technological and industrial applications and studied as model
systems in physics and material sciences. They are easily fluidized by applying
a mechanical stress, undergoing a yielding transition that still lacks a
unified description. Here, we investigate yielding in three classes of
repulsive soft solids, using analytical and numerical modelling and experiments
probing the microscopic dynamics and mechanical response under oscillatory
shear. We find that at the microscopic level yielding consists in a transition
between two distinct dynamical states, which we rationalize by proposing a
lattice model with dynamical coupling between neighboring sites, leading to a
unified state diagram for yielding. Leveraging the analogy with Wan der Waals's
phase diagram for real gases, we show that distance from a critical point plays
a major role in the emergence of first-order-like vs second-order-like features
in yielding, thereby reconciling previously contrasting observations on the
nature of the transition.
