As infrastructure confront rapidly changing environments, there is an immediate need to provide the flexibility to pivot resources and how infrastructures are prioritized. Yet infrastructures are often categorized based on static criticality framings. We describe dynamic criticality as the flexibility and reprioritization of infrastructure and resources during disturbances. We find that the most important prerequisite for dynamic criticality is organizational adaptive capacity through resilience in goals, structures, sensemaking, and strategies. Dynamic capabilities are increasingly important in the Anthropocene, where accelerating conditions, uncertainty, and growing complexity are challenging infrastructures. We review sectors that deployed dynamic management approaches amidst changing disturbances: leadership and organizational change, defense, medicine, manufacturing, and disaster response. We use an inductive thematic analysis to identify key themes and competencies and analyze capabilities that describe dynamic criticality. These competencies drive adaptive capacity and open up the flexibility to pivot what is deemed critical, depending on the particulars of the hazard. We map these competencies to infrastructure systems and describe how infrastructure organizations may build adaptive capacity toward flexible priorities.