The human brain is notably different from that of other primate species by its size and structure, in addition to its behavioral output. As we seek to understand how the human brain has evolved, many researchers have turned to genomics to help elucidate the biological basis for uniqueness of the human brain. When considering the molecular evolution of the human brain, a common misconception is that molecular evolution should be “unidirectional”—progressing along a single trajectory with the human brain as the ultimate goal. This outlook fails to acknowledge the importance of variability in the evolutionary process. In this review, we review what we know about inter- and intraspecific molecular diversity in the human brain arising from heritable and non-heritable sources. We note that genetic substitutions may not be optimal in brain evolution due to pleiotropic effects. Instead, we focus on other sources of molecular diversity including gene duplications, copy number variations, and transcriptional regulation. With recent advancements in the field of single-cell genomics, we explore what is currently known about gene expression at the cellular level and highlight opportunities to advance our understanding of human uniqueness at the neuronal level.