  We review the aging phenomenon in the context of the simplest trap model,
Bouchaud's REM-like trap model, from a spectral theoretic point of view. We
show that the generator of the dynamics of this model can be diagonalized
exactly. Using this result, we derive closed expressions for correlation
functions in terms of complex contour integrals that permit an easy
investigation into their large time asymptotics in the thermodynamic limit. We
also give a ``grand canonical'' representation of the model in terms of the
Markov process on a Poisson point process. In this context we analyze the
dynamics on various time scales.
