Creativity is a complex construct that would benefit from a more comprehensive mechanistic approach. Two processes have been defined to be central to creative cognition: divergent and convergent thinking. These two processes are most often studied using the Alternate Uses Test (heavily relying on divergent thinking), and the Remote Associates Test (heavily relying on convergent thinking, at least with analytical solutions). Although creative acts should be regarded compound processes, most behavioral and neuroimaging studies ignore the composition of basic operations relevant for the task they investigate. In order to provide leverage for a more mechanistic, and eventually even comprehensive computational, approach to creative cognition, we compare findings from divergent and convergent thinking studies and review the similarities and differences between the two underlying types of processes, from a neurocognitive perspective with a strong focus on cortical structures. In this narrative review, we discuss a broad scope of neural correlates of divergent and convergent thinking. We provide a first step towards theoretical integration, by suggesting that creative cognition in divergent- and convergent-thinking heavy tasks is modulated by metacontrol states, where divergent thinking and insight solutions in convergent-thinking tasks seem to benefit from metacontrol biases towards flexibility, whereas convergent, analytical thinking seems to benefit from metacontrol biases towards persistence. These particular biases seem to be reflected by specific cortical brain-activation patterns, involving left frontal and right temporal/parietal networks. Our tentative framework could serve as a first proxy to guide neuroscientific creativity research into assessing more mechanistic details of human creative cognition.