The Precambrian world, biologically speaking, was remarkably simple and populated exclusively by microbes. In sharp contrast, our contemporary biological world is perceived as remarkably diverse and complex. What were the processes that facilitated the emergence of biological complexity from simplicity during the course of Earth's history? They would certainly include (a) the major transitions in evolution, such as the emergence of oxygenic photosynthesis and aerobic respiration, supported by a benign geochemistry that enabled evolutionary processes; (b) the leap in biological complexity from prokaryotes to unicellular and then multicellular eukaryotes, which led to phagotrophy and the evolution of food chains; and (c) establishment of an elevated and stable atmospheric oxygen tension that molded a biosphere capable of supporting large, complex organisms and their evolutionary radiations. Here, we attempt to analyze the fundamental reality of biological complexity by tracing the path from microbes in Earth's early anoxic atmosphere to the biological complexity of the contemporary aerobic biosphere, which is apparently more complex than life in the early Precambrian. [ABSTRACT FROM AUTHOR]