With the improvement of analytical methods and the development of thermal ionisation mass spectrometry (TIMS) and multiple-collector inductively coupled plasma mass spectrometry (MC-ICP-MS), the researches on geochemistry of non-traditional stable isotopes(Cu, Zn, Fe, Se, Mo, Cr, Hg) have made tremendous progress in the past ten years. Redox conditions are the primary reasons for Mo isotope fractionation, so Mo isotopic fractionation has been successfully employed to explain the evolution of paleo-environment. Mo isotopic fractionation studies have yielded considerable results in explaining ore fluids in ore deposits and Mo cycling in ocean. Mo stable isotope geochemistry is therefore becoming a new frontier subject in earth sciences. Based on summarizing the previous researches and synthesizing the authors' results of Mo isotope studies, this paper deals with the main advances in the study of Mo stable isotopes with the particular emphasis placed on the separation of Mo from the sample, the determination method and correction for instrumental mass-dependent isotopic fractionation of the isotope tracer sample, and the application prospects of the Mo stable isotopes in earth sciences.