Species worldwide are subject to contractions in both abundance and geographical range, and their persistence in a changing environment may thus depend on the ability to survive in small and fragmented populations. Despite the urgent need to understand how extinction works, our knowledge of pre-extinction genetic processes is limited because techniques allowing population and conservation genomics to be studied in wild threatened populations have become available only recently. In this thesis, I used the last surviving population of the woolly mammoth (Mammuthus primigenius) as a model for studying pre-extinction population dynamics. I used ancient DNA as a tool to study microevolutionary processes in real time, analysing genetic changes in response to environmental shifts at the end of the last Ice Age and exploring impacts of genetic drift and inbreeding as woolly mammoths became isolated on Wrangel Island and survived for 6000 years at small population size. Using mitochondrial genomes, I found evidence of a founder effect that decreased the maternal diversity to a single lineage at the time when mammoths became trapped on Wrangel Island (~10,500 years ago). Moreover, a two- to three-fold higher mitochondrial mutation rate in Holocene and a fixed, potentially detrimental mutation in the ATP6 gene encoding for one of the key enzymes of the oxidative phosphorylation pathway, is consistent with the hypothesis that selection is less effective in removing deleterious mutations in small populations. A loss of diversity was also observed in an immunity gene that belongs to the major histocompatibility complex (MHC), even though the MHC is considered to be under balancing selection. Low-coverage genomic data was analysed in order to estimate endogenous DNA content and molecular sex of the mammoth samples. The observation of a male bias (69%) in the sex ratio led to the conclusion that male mammoths were more likely to die in a way that ensured good preservation. Another potential way of getting information about life history strategies of extinct species, which was explored here, is by measuring testosterone levels in mammoth hair shafts in connection with molecular sex inference. Finally, given that previous estimates have suggested a very small Holocene effective population size on Wrangel Island and thus that the population may have been too small to avoid genome erosion, four mammoths were sequenced to a high coverage in order to look for genomic consequences of small population size. When compared to mammoths from the Pleistocene mainland population, Wrangel Island mammoths had lower levels of genome-wide diversity and had a higher proportion of their genomes allocated in runs of homozygosity, which are large fragments completely depleted of diversity. Importantly, genome erosion appears to have accelerated in the last ten generations before the extinction, resulting in the last known woolly mammoth having almost 40% of its genome without any genetic diversity. Overall, these results highlight how genetic drift and inbreeding triggered genomic deterioration in the last surviving woolly mammoth population. Although Wrangel Island was a refugium, where mammoths survived for thousands of years after the last Ice Age, and the causal factors of the final extinction are not yet clear, isolation and small population size without any possibility of new gene flow may have contributed to reduced fitness, and thus to extinction.