Creative cognition is the driving force behind all cultural and scientific progress. In recent years, the field of neurocognitive creativity research (NCR) has made considerable progress in revealing the neural and psychological correlates of creative cognition. However, a detailed understanding of how cognitive processes produce creative ideas, and how these processes interact differently across tasks and individuals, remains elusive. In this article, we argue that the increased adoption of computational modeling can help greatly in achieving this goal. While the verbal theories guiding NCR have evolved from broader accounts into more specific descriptions of neurocognitive processes, they remain more open to interpretation and harder to falsify than formal models. Translating theories into computational models can make them more concrete, accessible, and easier to compare, and helps researchers to develop causal hypotheses for how variation in cognitive factors leads to variation in creative outcomes. Currently, however, computational modeling of creativity is conducted almost entirely separately from NCR, and few attempts have been made to embody the cognitive theories of NCR in models that can simulate performance on common lab-based tasks. In this paper, we discuss theories of creative cognition and how they might benefit from the wider adoption of formal modeling. We also examine recent computational models of creativity and how these might be improved and better integrated with NCR. Finally, we describe a pathway toward a mechanistic understanding of creative cognition through the integration of computational modeling, psychological theory, and empirical research, outlining an example model based on dual-process accounts
