All morphologically complex life on Earth, beyond the level of cyanobacteria, is eukaryotic. All eukaryotes share a common ancestor that was already a complex cell. Despite their biochemical virtuosity, prokaryotes show little tendency to evolve eukaryotic traits or large genomes. Here I argue that prokaryotes are constrained by their membrane bioenergetics, for fundamental reasons relating to the origin of life. Eukaryotes arose in a rare endosymbiosis between two prokaryotes, which broke the energetic constraints on prokaryotes and gave rise to mitochondria. Loss of almost all mitochondrial genes produced an extreme genomic asymmetry, in which tiny mitochondrial genomes support, energetically, a massive nuclear genome, giving eukaryotes three to five orders of magnitude more energy per gene than prokaryotes. The requirement for endosymbiosis radically altered selection on eukaryotes, potentially explaining the evolution of unique traits, including the nucleus, sex, two sexes, speciation, and aging.