Twin and family studies have demonstrated that most cognitive traits are moderately to highly heritable. Neurodevelopmental disorders such as dyslexia, autism, and specific language impairment (SLI) also show strong genetic influence. Nevertheless, it has proved difficult for researchers to identify genes that would explain substantial amounts of variance in cognitive traits or disorders. Although this observation may seem paradoxical, it fits with a multifactorial model of how complex human traits are influenced by numerous genes that interact with one another, and with the environment, to produce a specific phenotype. Such a model can also explain why genetic influences on cognition have not vanished in the course of human evolution. Recent linkage and association studies of SLI and dyslexia are reviewed to illustrate these points. The role of nonheritable genetic mutations (sporadic copy number variants) in causing autism is also discussed. Finally, research on phenotypic correlates of allelic variation in the genes ASPM and microcephalin is considered; initial interest in these as genes for brain size or intelligence has been dampened by a failure to find phenotypic differences in people with different versions of these genes. There is a current vogue for investigators to include measures of allelic variants in studies of cognition and cognitive disorders. It is important to be aware that the effect sizes associated with these variants are typically small and hard to detect without extremely large sample sizes.