Conviction Narrative Theory (CNT) is a theory of choice under radical uncertainty—situations where outcomes cannot be enumerated and probabilities cannot be assigned. Whereas most theories of choice assume that people rely on (potentially biased) probabilistic judgments, such theories cannot account for adaptive decision-making when probabilities cannot be assigned. CNT proposes that people use narratives—structured representations of causal, temporal, analogical, and valence relationships—rather than probabilities, as the currency of thought that unifies our sense-making and decision-making faculties. According to CNT, narratives arise from the interplay between individual cognition and the social environment, with reasoners adopting a narrative that feels ‘right’ to explain the available data; using that narrative to imagine plausible futures; and affectively evaluating those imagined futures to make a choice. Evidence from many areas of the cognitive, behavioral, and social sciences supports this basic model, including lab experiments, interview studies, and econometric analyses. We propose 12 principles to explain how the mental representations (narratives) interact with four inter-related processes (explanation, simulation, affective evaluation, communication), examining the theoretical and empirical basis for each. We conclude by discussing how CNT can provide a common vocabulary for researchers studying everyday choices across areas of the decision sciences.