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The U–Th chronometer has revolutionized Quaternary science in the last few decades and can now be considered a well-established, mature technique with growing application in archaeology as an alternative to 14 C dating and OSL, reaching well beyond the cutoff for both these methods. Applying the U–Pb technique to material within a time frame of interest to archaeology is a challenge only recently overcome, with enormous potential for future development and use. In terms of range, U–Th can generally date material of between a few years and as much as 600 ka, while U–Pb is best suited to material of 1 million years and older. U–Th dating is typically precise, with error margins of better than 1% routinely achievable for material of the last interglacial age or younger. Carbonates are the most desirable U-series target material, with closed system behaviour being particularly important for U–Th dating; making inorganic deposits such as speleothems (secondary cave carbonates), tufa and calcrete ideal. Some biogenic carbonates such as coral and eggshell are often amenable to U-series dating, but less ideal material such as fossil teeth, bone and mollusc shell usually continue to gain uranium after deposition meaning accurate ages cannot be calculated. In all cases, the importance of a thorough understanding of the context of dated material cannot be overstated. In this contribution we review U–Th and U–Pb dating through an archaeological lens, focussing on the methods themselves; how to best interpret published data and how best to avoid common pitfalls.