Ideas about atmospheric composition and climate on the early Earth have evolved considerably over the last 30 years, but many uncertainties still remain. It is generally agreed that the atmosphere contained little or no free oxygen initially and that oxygen concentrations increased markedly near 2.0 billion years ago, but the precise timing of and reasons for its rise remain unexplained. Likewise, it is usually conceded that the atmospheric greenhouse effect must have been higher in the past to offset reduced solar luminosity, but the levels of atmospheric carbon dioxide and other greenhouse gases required remain speculative. A better understanding of past atmospheric evolution is important to understanding the evolution of life and to predicting whether Earth-like planets might exist elsewhere in the galaxy.