Life on earth began some 4 billion years ago, but then got stuck at the level of bacteria for more than 2 billion years. The complex ‘eukaryotic’ cell arose abruptly in a singular event around 1.5–2 billion years ago. All eukaryotes share a long list of complex traits, from the nucleus to sex and senescence, which are all but unknown in bacteria. Why are humans so similar to mushrooms at the level of cells, even though we live so differently? Why did evolution follow such a peculiar trajectory? The answers might lie in the equally strange mechanism by which all cells generate ATP: chemiosmotic coupling.