The unique qualities of the human brain are a product of a complex evolutionary process. Evolution, famously described by François Jacob as a “tinkerer,” builds upon existing genetic elements by modifying and repurposing them for new functions. Genetic changes in DNA may lead to the emergence of new genes or cause altered gene expression patterns. Both gene and regulatory element mutations may lead to new functions. Yet, this process may lead to side-effects. An evolutionary trade-off occurs when an otherwise beneficial change, which is important for evolutionary success and is under strong positive selection, concurrently results in a detrimental change in another trait. Pleiotropy occurs when a gene affects multiple traits. Antagonistic pleiotropy is a phenomenon whereby a genetic variant leads to an increase in fitness at one life-stage or in a specific environment, but simultaneously decreases fitness in another respect. Therefore, it is conceivable that the molecular underpinnings of evolution of highly complex traits, including brain size or cognitive ability, under certain conditions could result in deleterious effects, which would increase the susceptibility to psychiatric or neurodevelopmental diseases. Here, we discuss possible trade-offs and antagonistic pleiotropies between evolutionary change in a gene sequence, dosage or activity and the susceptibility of individuals to autism spectrum disorders and schizophrenia. We present current knowledge about genes and alterations in gene regulatory landscapes, which have likely played a role in establishing human-specific traits and have been implicated in those diseases.