The climatic fluctuations of the Late Pleistocene likely had a large impact on the evolutionary history of Arctic species. Palaeogenomics is a useful tool to shed light on how past populations responded to these climatic shifts and the associated ice sheet dynamics and sea level change. Here, I have used modern and ancient DNA data from four Arctic mammals in order to investigate the impacts of Late Pleistocene climate on their evolutionary histories, from population dynamics and demography, to speciation and gene flow, adaptation, and genome erosion. In Paper I, using ancient mitogenomes from across their Late Pleistocene range, I showed that the Eurasian collared lemming (Dicrostonyx torquatus) had a dynamic Late Pleistocene population structure in Europe. Furthermore, the Eemian interglacial likely led to a bottleneck in collared lemmings, after which the species diversified during the Last Glacial period. Nuclear genome data from a modern individual in northeastern Siberia suggests population stability in northeastern Siberia during the Holocene. In Paper II, I sequenced the nuclear genome of a ~18,500 year old woolly rhinoceros (Coelodonta antiquitatis) and used this in combination with mitochondrial data to explore the demographic history of the species. There was little geographic structuring in the northeast Siberian population, and stability in their effective population size just prior to extinction, which may indicate a subsequent rapid decline towards extinction, likely associated with the Bølling-Allerød interstadial. Additionally, I found that this species had mutations in TRPA1, a gene involved in temperature sensitivity. In a third study (Paper III), I used whole genome data from modern and ancient true lemmings (Lemmus sp.) to determine that the Norwegian lemming (L. lemmus) has one of the youngest speciation times (~37-34 ka BP) of mammals. Norwegian lemmings have mutations in genes involved in coat colour, colour perception, fat transport and reproduction, and likely evolved their unique colouration as a result of isolation after the recolonisation of Fennoscandia. Finally, we examined the consequences of long-term small effective population size in muskox (Ovibos moschatus) using 107 modern nuclear genomes and one 21,000 year old Siberian genome (Paper IV). While muskox survived the warming at the end of the Late Pleistocene, the successive founder events experienced during its colonisation of the Canadian Arctic and Greenland reduced the genetic diversity to some of the lowest values observed in mammals. However, the results suggest that the long-term small population size likely led to purging of strongly deleterious alleles in the muskox, allowing them to persist to today with limited evidence of inbreeding depression. From a technical point, this thesis presents four de-novo genome assemblies, and the first whole nuclear genomes for these Arctic species. Taken together, the results in this thesis show that the climatic fluctuations, in particular the Eemian interglacial and Bølling-Allerød interstadial, along with sea level change and the formation and retreat of ice sheets during the Last Glacial Maximum have influenced the evolutionary histories of these four Arctic mammals.