The ¹⁷⁶Lu-¹⁷⁶Hf isotope method and its applications in earth sciences are discussed. Greater fractionation of Lu/Hf than Sm/Nd in planetary magmatic processes makes ¹⁷⁶Hf¹⁷⁷Hf a powerful geochemical tracer. In general, proportional variations of ¹⁷⁶Hf¹⁷⁷Hf exceed those of ¹⁴³Nd¹⁴⁴Nd by factors of 1.5–3 in terrestrial and lunar materials. Lu-Hf studies therefore have a major contribution to make in understanding of terrestrial and other planetary evolution through time, and this is the principal importance of Lu-Hf. New data on basalts from oceanic islands show unequivocally that whereas considerable divergences occur in ¹⁷⁶Hf¹⁷⁷Hf-⁸⁷Sr⁸⁶Sr and ¹⁴³Nd¹⁴⁴Nd-⁸⁷Sr⁸⁶Sr diagrams, ¹⁷⁶Hf¹⁷⁷Hf and 1⁴³Nd¹⁴⁴Nd display a single, linear isotopic variation in the suboceanic mantle. These discordant ⁸⁷Sr⁸⁶Sr relationships may allow, with the acquisition of further Hf-Nd-Sr isotopic data, a distinction between processes such as mantle metasomatism, influence of seawater-altered material in the magma source, or recycling of sediments into the mantle. In order to evaluate the Hf-Nd isotopic correlation in terms of mantle fractionation history, there is a need for measurements of Hf distribution coefficients between silicate minerals and liquids, and specifically for a knowledge of Hf behavior in relation to rareearth elements. For studying ancient terrestrial Hf isotopic variations, the best quality Hf isotope data are obtained from granitoid rocks or zircons. New data show that very U-Pb discordant zircons may have upwardly-biased ¹⁷⁶Hf¹⁷⁷Hf, but that at least concordant to slightly discordant zircons appear to be reliable carriers of initial ¹⁷⁶Hf¹⁷⁷Hf. Until the controls on addition of radiogenic Hf to zircon are understood, combined zircon-whole rock studies are recommended. Lu-Hf has been demonstrated as a viable tool for dating of ancient terrestrial and extraterrestrial samples, but because it offers little advantage over existing methods, is unlikely to find wide application in pure chronological studies.