  The purpose of this article is to construct a toolbox, in Dynamical Systems,
to support the idea that ``whenever we can prove a limit theorem in the
classical sense for a dynamical system, we can prove a suitable almost-sure
version based on an empirical measure with log-average''. We follow three
different approaches: martingale methods, spectral methods and induction
arguments. Our results apply among others to Axiom A maps or flows, to systems
inducing a Gibbs-Markov map and to the stadium billiard.
