There is substantial new variation for quantitative traits generated by mutation that can be utilised by artificial selection. With long-term selection, however, response is often attenuated and a selection limit sometimes reached, even though genetic variation is frequently still present in these lines. In this paper, the theoretical bases of long-term response and variability of populations that come from mutational variance are reviewed, and the relation between them is related to the strength and mode of the natural selection, whether due to pleiotropic effects of mutant genes or stabilising selection. Simple formulae to predict the consequence of relaxed or reversed selection are derived. Results from long-term selection experiments in mice in this laboratory are described and related to the theoretical analyses with the aim of reconciling the evidence for substantial standing variation with the low rate of response.