Microbiology has unraveled rich evidence of ongoing reticulate evolutionary processes and complex interactions both within and between cells. These phenomena feature real biological networks, which can logically be analyzed using network-based tools. It is thus not surprising that network sciences, a field independent from evolutionary biology and microbiology, have recently pervasively infused their methods into both fields. Importantly, network tools bring forward observations enhancing the understanding of three core evolutionary concepts: variation, fitness, and heredity. Consequently, our work shows how network sciences can enhance evolutionary theory by explaining the evolution by natural selection of a broad diversity of units of selection, while updating the popular figure of Darwin's tree of life with a comprehensive sketch of the networks of evolution.