Although most of us are critical of gender stereotypes, few deny the existence of two discrete biological sexes. Yet biology shows us dozens of combinations of human sex chromosomes, and neuroscience that the brains of men and women are not distinctive, but a mosaic of variation. Could biological sex itself be an illusion constructed by human categories? Can we overcome or refashion these categories to suit twenty-first century needs? Or is this a futile attempt to deny the reality of two biological sexes?