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BACKGROUND: Mircobeam Lu-Hf isotopic analysis on minerals provides an important means to understand the microscopic process of magmatic activity and metamorphic reaction and to trace provenance of sediment, which greatly promotes the development of petrogeochemistry. Many methods were provided to obtain accurate and precise microbeam Lu - Hf isotopic data, and many mineral standards for microbeam Lu - Hf isotopic analysis were developed. OBJECTIVES: To review and understand the microbeam methods for Lu-Hf isotopic analysis. METHODS: Systematic compilations of published data of standards and discussion on the different methods for microbeam Lu-Hf isotopic analysis. RESULTS: The development history of microbeam Lu-Hf isotopic analysis in the past 30 years is reviewed, and the influence of 176Yb and 176Lu isobars, REE oxides, and Ta-rich matrices on the precision and accuracy of Hf isotope measurement is systematically evaluated as well as the different correction strategies and programs provided in previous studies. In addition, a comprehensive compilation of the different Yb and Lu isotopic compositions reported in references and the different methods of microbeam Lu-Hf isotopic analyses on various Hf-rich minerals such as zircon, baddeleyite, zirconolite, zirkelite, calzirtite, eudialyte, rutile, cassiterite, and columbite-group minerals is made. The micro-drill/ micro-saw sampling Lu-Hf isotopic analysis of Lu-rich minerals has played an important role in revealing the multi-stage orogenic process and the duration of mineral growth. The advent of laser ablation inductively coupled plasma triple quadrupole mass spectrometry (LA-ICP-Q-MS/ MS) has increased the spatial resolution of Lu-Hf single-spot/ isochron dating analysis of Lu-rich minerals to the micrometer scale. This method relies on the collision reaction of Hf and NH3 to realize the online separation of Hf from Lu, and achieves the purpose of synchronous measurement of 176Lu/ 177Hf and 176Hf/ 177Hf ratios, which is introduced in detail. CONCLUSIONS: The new generation of tandem multi-collector sector field mass spectrometer with collision/ reaction cell has high stability and sensitivity, which can be used to determine online separation of Hf from REEs, produce high-precision Hf isotope measurements for high Yb/ Hf or Ta-rich minerals under high spatial resolution conditions, and significantly improve the precision and accuracy of microbeam Lu -Hf isotopic analysis. This deserves extensive attention in the future. [ABSTRACT FROM AUTHOR]