In popular imagination creativity requires us to surrender control. Yet, attention is at the heart of control, and many studies show attention to play a key role in the creative process. This is partly due to the selective nature of attention—creative cognition consists of two phases, idea generation and idea evaluation, and selective processes are essential for both phases. Here, we investigate attentional (i.e., selective) mechanisms underlying each phase, using the framework of two major attention taxonomies: top-down/bottom-up and internal/external attention. (...) We argue that creative cognition is supported by a dynamic interplay between the typically opposing sides of each taxonomy. Further, we argue that this dynamic relationship is reflected in interactions across three large-scale brain networks: the default mode (DMN), frontoparietal control (FPN), and salience (SN) networks. Our review of the evidence suggests that creative cognition is best achieved through the flexible use of multiple forms of attention, rather than through reduced attention. We thus propose a two-dimensional space, including one dimension for top-down/bottom-up and another for internal/external attention, which can sufficiently capture the flexibility and diversity of attentional mechanisms underlying different stages and components of creative cognition. (shrink)