The review discusses, in a format of a timeline, the studies of different types of genetic variants, present in Homo sapiens, but absent in all other primate, mammalian, or vertebrate species, tested so far. The main characteristic of these variants is that they are found in regions of high evolutionary conservation. These sequence variations include single nucleotide substitutions (called human accelerated regions), deletions, and segmental duplications. The rationale for finding such variations in the human genome is that they could be responsible for traits, specific to our species, of which the human brain is the most remarkable. As became obvious, the vast majority of human-specific single nucleotide substitutions are found in noncoding, likely regulatory regions. A number of genes, associated with these human-specific alleles, often through novel enhancer activity, were in fact shown to be implicated in human-specific development of certain brain areas, including the prefrontal cortex. Human-specific deletions may remove regulatory sequences, such as enhancers. Segmental duplications, because of their large size, create new coding sequences, like new functional paralogs. Further functional study of these variants will shed light on evolution of our species, as well as on the etiology of neurodevelopmental disorders.