Lest the term “gullibility” remains confined to moralistic judgment, theoretical work is needed to elaborate the concept and to ground it in psychological science. Attempting to make progress in this direction, we review instances of gullibility from various perspectives on inductive reasoning (Humean, Bayesian, Pascalian). The easy task is to represent gullibility as a special case of heuristic reasoning and predictable irrationality. The difficult task is to embed gullibility in a theory that describes successes and failures of reasoning under lawful conditions. Another difficulty is to identify the concept’s boundaries. Where does gullibility end? We use the issue of irrational trust as an example to explore whether this closely related concept may shed light on gullibility proper.