Ageing has become the paradigm to describe dynamical behavior of
glassy systems, and in particular spin glasses. Trap models have been
introduced as simple caricatures of effective dynamics of such
systems. In this talks I explain  recent results with G. Ben Arous and J.
Cerny that show that in a wide class of mean field models and on a
wide range of time scales, ageing occurs precisely as
predicted by the REM-like trap model of Bouchaud and Dean.