Abstract: The Precambrian extends over about 4 billion years from the formation of Earth to the beginning of the Cambrian (4.6 billion years ago to 0.54 billion years ago). Studying climate evolution over such a long period is really challenging, but fundamental and intriguing. It is difficult to comprehensively review progress of studies in Precambrian climate evolution. Three important issues are chosen and discussed, which are atmospheric evolution, two extremely cold periods with global-scale glaciations, and the faint young Sun paradox. For atmospheric evolution, tendencies of atmospheric evolution are briefly reviewed, and three important processes involved in atmospheric evolution are introduced, which are atmospheric escape, two rapid increases of atmospheric oxygen, and the carbonate-silicate cycle and its negative feedback to climate. Two global-scale glaciations intervals happened at the Paleoproterozoic (2.4 billion years ago to 2.1 billion years ago) and the Neoproterozoic (0.8 billion years ago to 0.58 billion years ago). Mechanisms of formation and deglaciation of the two global glaciations are reviewed. The faint young Sun paradox is a classical topic in Earth’s early climate studies. Here, most recent results are summarized.

Key words: atmospheric evolution, Earth evolution, life evolution, snowball Earth, faint young Sun paradox