  We survey the recent mathematical results about aging in certain simple
disordered models. We start by the Bouchaud trap model. We then survey the
results obtained for simple models of spin-glass dynamics, like the REM (the
Random Energy Model, which is well approximated by the Bouchaud model on the
complete graph), then the spherical Sherrington-Kirkpatrick model. We will
insist on the differences in phenomenology for different types of aging in
different time scales and different models. This talk is based on joint works
with A.Bovier, J.Cerny, A.Dembo, V.Gayrard, A.Guionnet, as well as works by
C.Newman, R.Fontes, M.Isopi, D.Stein.
