A worrying number of psychological findings are not replicable. Diagnoses of the causes of this “replication crisis,” and recommendations to address it, have nearly exclusively focused on methods of data collection, analysis, and reporting. We argue that a further cause of poor replicability is the often weak logical link between theories and their empirical tests. We propose a distinction between discovery-oriented and theory-testing research. In discovery-oriented research, theories do not strongly imply hypotheses by which they can be tested, but rather define a search space for the discovery of effects that would support them. Failures to find these effects do not question the theory. This endeavor necessarily engenders a high risk of Type I errors—that is, publication of findings that will not replicate. Theory-testing research, by contrast, relies on theories that strongly imply hypotheses, such that disconfirmation of the hypothesis provides evidence against the theory. Theory-testing research engenders a smaller risk of Type I errors. A strong link between theories and hypotheses is best achieved by formalizing theories as computational models. We critically revisit recommendations for addressing the “replication crisis,” including the proposal to distinguish exploratory from confirmatory research, and the preregistration of hypotheses and analysis plans.