An oxygen-rich atmosphere is essential for complex animals. The early Earth had an anoxic atmosphere, and understanding the rise and maintenance of high O2 levels is critical for investigating what drove our own evolution and for assessing the likely habitability of exoplanets. A growing number of techniques aim to reproduce changes in O2 levels over the Phanerozoic Eon (the past 539 million years). We assess these methods and attempt to draw the reliable techniques together to form a consensus Phanerozoic O2 curve. We conclude that O2 probably made up around 5–10% of the atmosphere during the Cambrian and rose in pulses to ∼15–20% in the Devonian, reaching a further peak of greater than 25% in the Permo-Carboniferous before declining toward the present day. Evolutionary radiations in the Cambrian and Ordovician appear consistent with an oxygen driver, and the Devonian “Age of the Fishes” coincides with oxygen rising above 15% atm. ▪An oxygen-rich atmosphere is essential for complex animals such as humans. ▪We review the methods for reconstructing past variation in oxygen levels over the past 539 million years (the Phanerozoic Eon). ▪We produce a consensus plot of the most likely evolution of atmospheric oxygen levels. ▪Evolutionary radiations in the Cambrian, Ordovician, and Devonian periods may be linked to rises in oxygen concentration.