Evolutionary perspective is critical for understanding human biology, human medicine, and the traits that make human beings unique. One of the crucial characteristics that sets humans apart from other extant species is our cognitive ability, which allows for complex processes including symbolic thought, theory of mind, and syntactical-grammatical language, and is thought to arise from the expansion and specialization of the human nervous system. It has been hypothesized that the same evolutionary changes that allowed us to develop these valuable skills made humans susceptible to neurodevelopmental and neurodegenerative disease. Unfortunately, our lack of access to our extinct ancestors makes this a difficult hypothesis to test, but recent collaborations between the fields of evolution, genetics, genomics, neuroscience, neurology and psychiatry have begun to provide some clues. Here, we will outline recent work in those fields that have utilized our growing knowledge of disease risk genes and loci, identified by wide-scale genetic studies, and nervous system development and function to draw conclusions about the impact of human-specific aspects of evolution. We will discuss studies that assess evolution at a variety of scales including at the levels of whole brain regions, cell types, synapses, metabolic processes, gene expression patterns, and gene regulation. At all of these levels, there is preliminary evidence that human-specific brain features are linked to neurodevelopmental and neurodegenerative disease risk.