Due to past and current climatic changes, range contractions and range shifts are essential stages in the history of a species. However, unlike range expansions, the molecular consequences of these processes have been little investigated. In order to fill this gap, we simulated patterns of molecular diversity within and between populations for various types of range contractions and range shifts. We show that range contractions tend to decrease genetic diversity as compared with population with stable ranges but quite counterintuitively fast range contractions preserve higher levels of diversity and induce lower levels of genetic differentiation among refuge areas than slow contractions. Contrastingly, fast range shifts lead to lower levels of diversity than slow range shifts. At odds with our expectations, we find that species actively migrating toward refuge areas can only preserve higher levels of diversity in refugia if the contraction is rapid. Under slow range contraction or slow range shift, active migration toward refugia lead to a larger loss of diversity as compared with scenarios with isotropic migration and may thus not be a good evolutionary strategy. These results suggest that the levels of diversity preserved after a climate change both within and between refuge areas will not only depend on the dispersal abilities of a species but also on the speed of the change. It also implies that a given episode of climatic change will impact differently species with different generation times.