Although molecular oxygen (O₂) is a major component of Earth’s atmosphere today and a key signature of life on this planet, we do not understand why and how Earth has evolved from the ancient oxygen-deficient world to the modern oxygen-rich environment, and whether a similar in-crease can be expected on other planets. This thesis provides a theory to answer this fundamental but unsolved question in Earth science. In the modern environment, atmospheric O₂ is maintained at a stable level due to the existence of negative feedback mechanisms. However, this brings us to a conundrum: under the regulation of negative feedbacks, how could O₂ concentrations have risen? This thesis suggests that the expansion of oxidative metabolisms provided a positive feed-back responsible for Earth’s oxygenation. This may appear counterintuitive: oxidative metabolic processes, after all, consume O₂. A potentially important positive feedback nevertheless lies in partially-oxidized organic matter (POOM) produced by oxidative metabolisms in sedimentary environments. This positive feedback derived from oxidative metabolisms is demonstrated via a mathematical model in this thesis. Its relevance to the rise of atmospheric O₂ crucially depends on the existence of POOM-producing oxidative metabolism(s) at the time of Earth’s oxygenation(s). One group of enzymes that can catalyze the formation of oxidative metabolic products is the oxygenase family. The methods of molecular phylogenomics are applied to reconstruct the evolutionary history of a representative oxygenase family; the results support such a relevance. Finally, this thesis constructs a mathematical model of Earth’s oxygen and carbon cycles and explores the dynamics of these two cycles during oxygenation events. From the perspective of non linear dynamics, this mathematical model interprets Earth’s oxygenations as dynamical bifurcations of the oxygen cycle and the accompanying excursions in carbon isotope records as the characteristic fluctuations associated with dynamical bifurcations. Collectively, the physical reasoning, phylogenomic analyses, and mathematical modeling in this thesis suggest an unstable evolution of Earth’s oxygen and carbon cycles in deep time.Ph.D.