The presence of many metastable states in disordered systems is directly responsible of  the slow down of dynamics at low temperatures and the consequent fall out of equilibrium causing, e.g., aging.  Mean-field models like the Sherrington-Kirkpatrick model for properly said amorphous magnets or like the p-spin interacting models for structural glasses are known to display qualitatively different properties both at the dynamic and the static level.
Such differences can be better understood looking at the number of the metastable states, i.e. at the complexity function, and at their stability.
Exploiting different analytical techniques and generalizing through different paths the concept of entropy in standard statistical mechanics we have investigated the behaviour of differently defined complexities in the above metioned models and made up a consistent scenario to clarify the structure of metastable states.