Successful adaptation helped the emergence of complexity. Alternating plastic- and rigid-like states were recurrently considered to play a role in adaptive processes. However, this extensive knowledge remained fragmented. In this paper I describe plasticity-rigidity cycles as a general adaptation mechanism operating in molecular assemblies, assisted protein folding, cellular differentiation, learning, memory formation, creative thinking, as well as the organization of social groups and ecosystems. Plasticity-rigidity cycles enable a novel understanding of aging, exploration/exploitation trade-off and evolvability, as well as help the design of efficient interventions in medicine and in crisis management of financial and biological ecosystems.