These notes are devoted to the study of mixing theory. The underlying goal is to provide statisticians dealing with problems involving weak dependence properties, with a powerful and easy tool. Up to now, this approach to dependence has been mainly considered from an abstract point of view. For an excellent review on this subject we refer to : "Dependence in Probability and Statistics, a Survey of Recent Results" ('). The aim of this work is to study applications of these results. We obtain bounds for the decay of mixing coefficient sequences associated to random processes or to random fields which are actually used in Statistics. In some cases we will give counterexamples which show that some frequently held ideas are wrong. In fact, it would be of little interest to study a probabilistic technique with no field of application.