Given that natural selection is so powerful at optimizing complex adaptations, why does it seem unable to eliminate genes (susceptibility alleles) that predispose to common, harmful, heritable mental disorders, such as schizophrenia or bipolar disorder? We assess three leading explanations for this apparent paradox from evolutionary genetic theory: (1) ancestral neutrality (susceptibility alleles were not harmful among ancestors), (2) balancing selection (susceptibility alleles sometimes increased fitness), and (3) polygenic mutation-selection balance (mental disorders reflect the inevitable mutational load on the thousands of genes underlying human behavior). The first two explanations are commonly assumed in psychiatric genetics and Darwinian psychiatry, while mutation-selection has often been discounted. All three models can explain persistent genetic variance in some traits under some conditions, but the first two have serious problems in explaining human mental disorders. Ancestral neutrality fails to explain low mental disorder frequencies and requires implausibly small selection coefficients against mental disorders given the data on the reproductive costs and impairment of mental disorders. Balancing selection (including spatio-temporal variation in selection, heterozygote advantage, antagonistic pleiotropy, and frequency-dependent selection) tends to favor environmentally contingent adaptations (which would show no heritability) or high-frequency alleles (which psychiatric genetics would have already found). Only polygenic mutation-selection balance seems consistent with the data on mental disorder prevalence rates, fitness costs, the likely rarity of susceptibility alleles, and the increased risks of mental disorders with brain trauma, inbreeding, and paternal age. This evolutionary genetic framework for mental disorders has wide-ranging implications for psychology, psychiatry, behavior genetics, molecular genetics, and evolutionary approaches to studying human behavior.