  The goal of this chapter is to review recent analytical results about the
growth of a (static) correlation length in glassy systems, and the connection
that can be made between this length scale and the equilibrium correlation time
of its dynamics. The definition of such a length scale is first given in a
generic setting, including finite-dimensional models, along with rigorous
bounds linking it to the correlation time. We then present some particular
cases (finite connectivity mean-field models, and Kac limit of finite
dimensional systems) where this length can be actually computed.
