The vast majority of research on autism spectrum disorder (ASD) focuses on characterizing and addressing the social communication deficits and restricted, repetitive patterns of behavior that constitute the diagnostic criteria for the disorder. Yet, a small but significant portion of individuals diagnosed with ASD exhibit exceptional cognitive abilities in one or more domains. These "twice-exceptional" individuals often have unique skills that enable them to make significant contributions to the workforce, while at the same time facing unique challenges during the transition to independent living due to a lack of services and broad public misperceptions regarding their condition. Here we review the current literature on cognitive divergence in ASD, focusing on cognitive theories, neural substrates, and clinical and societal implications for increasing understanding of this phenomenon.