  We investigate limit theorems for Birkhoff sums of locally H\"older functions
under the iteration of Gibbs-Markov maps. Aaronson and Denker have given
sufficient conditions to have limit theorems in this setting. We show that
these conditions are also necessary: there is no exotic limit theorem for
Gibbs-Markov maps. Our proofs, valid under very weak regularity assumptions,
involve weak perturbation theory and interpolation spaces. For L^2 observables,
we also obtain necessary and sufficient conditions to control the speed of
convergence in the central limit theorem.
