In adsorption processes of the liquid or gas phase, a particular dynamic adsorption behavior caused by the reversible mechanical deformation (expansion or contraction) of absorption materials driven by the host–guest interaction is called “flexible adsorption,” and the materials with this particular behavior can be called “flexible adsorption materials.” Flexible absorption materials, such as crosslinked polymers, have received much attention from researchers due to their flexible framework structure and specific adsorption kinetics. They have shown great potential in gas storage and other energy applications. This paper reviews recent advances in the definition, theoretical development, and classification of flexible absorption materials. Potential application examples of flexible absorption materials in gas/liquid absorption and separation, functional devices, and energy catalysis are analyzed to guide their development.