During the last decade, network approaches became a powerful tool to describe protein structure and dynamics. Here, we describe first the protein structure networks of molecular chaperones, then characterize chaperone containing sub-networks of interactomes called as chaperone-networks or chaperomes. We review the role of molecular chaperones in short-term adaptation of cellular networks in response to stress, and in long-term adaptation discussing their putative functions in the regulation of evolvability. We provide a general overview of possible network mechanisms of adaptation, learning and memory formation. We propose that changes of network rigidity play a key role in learning and memory formation processes. Flexible network topology provides learning competent state. Here, networks may have much less modular boundaries than locally rigid, highly modular networks, where the learnt information has already been consolidated in a memory formation process. Since modular boundaries are efficient filters of information, in the learning competent state information filtering may be much smaller, than after memory formation. This mechanism restricts high information transfer to the learning competent state. After memory formation, modular boundary-induced segregation and information filtering protect the stored information. The flexible networks of young organisms are generally in a learning competent state. On the contrary, locally rigid networks of old organisms have lost their learning competent state, but store and protect their learnt information efficiently. We anticipate that the above mechanism may operate at the level of both protein-protein interaction and neuronal networks.