Central limit theorems for correlated variables: some critical remarks

20 pages, 9 figures. Text at the basis of a talk presented at the 7th International Conference on Nonextensive Statistical Mechanics: Foundations and Applications (NEXT2008), Foz do Iguacu, Parana, Brazil, 27-31 October 2008International audienceIn this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in physics. Next, I show that there is room for new versions of central limit theorems applicable to specific classes of problems. Finally, I argue that we have insufficient evidence that, as a consequence of such a theorem, q-Gaussians occupy a special place in statistical physics