AbstractA view that has been gaining prevalence over the past decade is that the human conceptual system is malleable, dynamic, context‐dependent, and task‐dependent, that is, flexible. Within the flexible conceptual representation framework, conceptual representations are constructed ad hoc, forming a different, idiosyncratic instantiation upon each occurrence. In this review, we scrutinize the neurocognitive literature to better understand the nature of this flexibility. First, we identify some key characteristics of these representations. Next, we consider how these flexible representations are constructed by addressing some of the open questions in this framework: We review the age‐old question of how to reconcile flexibility with the apparent need for shareable stable definitions to anchor meaning and come to mutual understanding, as well as some newer questions we find critical, namely, the nature of relations among flexible representations, the role of feature saliency in activation, and the viability of all‐or‐none feature activations. We suggest replacing the debate about the existence of a definitional stable core that is obligatorily activated with a question of the degree and probability of activation of the information constituting a conceptual representation. We rely on published works to suggest that (1) prior featural salience matters, (2) feature activation may be graded, and (3) Bayesian updating of prior information according to current demands offers a viable account of how flexible representations are constructed. This proposal provides a theoretical mechanism for incorporating a changing momentary context into a constructed representation, while still preserving some of the concept's constituent meaning.