ABSTRACT The introduction of next‐generation sequencing methods has broadened the scope and utility of ancient DNA (aDNA) research, and is opening up exciting new applications in Quaternary science. Palaeogenomes – partial or complete genome sequences for extinct taxa – are now available for Neanderthals and Denisovans, various megafauna, and preserved microorganisms. The analysis of aDNA in sediments, including cores in which there are no visible macro‐ or microfossils, is helping to reconstruct past ecosystems, especially in Arctic regions where aDNA preservation is relatively good. In this review we follow the development of aDNA research over the last 30 years, showing how the problems caused by contamination of ancient samples with modern DNA have gradually been overcome, and highlighting those technical challenges that still exist. We then survey the current standing of palaeogenomics and sedimentary aDNA studies, and indicate how these fields might be developed further in coming years.