Dual process models of cognition suggest there are two kinds of thought: rapid, automatic Type 1 processes, and effortful, controlled Type 2 processes. Models of creative thinking also distinguish between two sets of processes: those involved in the generation of ideas, and those involved with their refinement, evaluation and/or selection. Here we review dual process models in both these literatures and delineate the similarities and differences. Both generative and evaluative creative processing modes involve elements that have been attributed to each of the dual processes of cognition. We explore the notion that creative thinking may rest upon the nature of a shifting process between generative and evaluative modes of thought. We suggest that through a synthesis application of the evidence bases on dual process models of cognition and from neuroimaging, together with developing chronometric approaches to explore the shifting process, could assist the development of interventions to facilitate creativity.