  In this paper we expose the results of our recent work on the dynamical TAP
approach to mean field glassy systems. Our aim is to clarify the connection
between free energy landscape and out of equilibrium dynamics in solvable
models. Frequently qualitative explanations of glassy behaviour are based on
the ``Free Energy Landscape Paradigm''. If its relevance for equilibrium
properties is clear, the relationship between free energy landscape and out of
equilibrium dynamics is not well understood yet. In this paper we clarify this
relationship for the class of spin glass models which reproduce
phenomenologically some features of structural glasses. The method we use is a
generalisation to dynamics of the Thouless, Anderson and Palmer approach to
thermodynamics of mean field spin glasses. Within this framework we show to
what extent the dynamics can be represented as an evolution in the free energy
landscape. In particular the relationship between the long-time dynamics and
the local properties of the free energy landscape shows up explicitly using
this approach.
