Primate evolution has been accompanied by complex reorganizations in brain anatomy and function. Little is known, however, about the relationship between anatomical and functional changes induced through primate evolution. Using functional magnetic resonance imaging, we assessed spatial and temporal correspondences of cortical networks in humans and monkeys. We provided evidence for topologically and functionally correspondent networks in sensory-motor and attention regions. More specifically, we revealed a possible monkey equivalent of the human ventral attention network. For other human networks, such as the language and the default-mode networks, we detected topological correspondent networks in the monkey, but with different functional signatures. Furthermore, we observed two lateralized human frontoparietal networks in the cortical regions displaying the greatest evolutionary expansion, having neither topological nor functional monkey correspondents. This finding may indicate that these two human networks are evolutionarily novel. Thus, our findings confirm the existence of networks where evolution has conserved both topology and function but also suggest that functions of structurally preserved networks can diverge over time and that novel, hence human-specific networks, have emerged during human evolution.