This chapter postulates the existence of two distinct yet, in practice, often blended modes of thought called possibility and actuality thinking and examines primarily the characteristics of the former. While a popular notion in education and, to some extent, in the psychology of creativity, ‘possibility thinking’ (PT) is reformulated here as a system of thought in its own right, focussed on explorations of ‘what could be’, ‘what is to come’, ‘what could have been’ and ‘what is not/will never be’. This proposition reflects a broader concern for the eminently human ability to engage with the possible, an issue reflected upon in a variety of fields of study, from narrative and play to creativity and wonder. In this chapter, a ‘cultural creative cognition’ lens is used to discuss PT as underpinned by four inter-related processes: pretence, anticipation, counterfactual and utopian thinking. Conclusions are drawn concerning the distinction between ‘wide’ and ‘narrow’ thought as modes that complement the more traditional division between ‘fast’ and ‘slow’ thinking and add an important new dimension to our understanding of creative cognition and of cognition in general: the capacity to build on while, at the same time, going beyond the experience of ‘what is’.