  In 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.
