Gene expression has been investigated in relation with growth rate in the yeast Saccharomyces cerevisiae, following different experimental strategies. The expression of some specific gene functional categories increases or decreases with growth rate. Our recently published results have unveiled that these changes in mRNA concentration with growth depend on the relative alteration of mRNA synthesis and decay, and that, in addition to this gene-specific transcriptomic signature of growth, global mRNA turnover increases with growth rate. We discuss here these results in relation with other previous and concurrent publications, and we add new evidence which indicates that growth rate controls mRNA turnover even under non-steady-state conditions.