Transitive inference has long been considered one of the hallmarks of human deductive reasoning. Recent reports of transitive-like behaviors in non-human animals have prompted a flourishing empirical and theoretical search for the mechanism(s) that may mediate this ability in non-humans. In this paper, I begin by describing the transitive inference tasks customarily used with non-human animals and then review the empirical findings. Transitive inference has been demonstrated in a wide variety of species, and the signature effects that usually accompany transitive inference in humans (the serial position effect and the symbolic distance effect) have also been found in non-humans. I then critically analyze the most prominent models of this ability in non-human animals. Some models are cognitive, proposing for instance that animals use the rules of formal logic or form mental representations of the premises to solve the task, others are based on associative mechanisms such as value transfer and reinforcement and non-reinforcement. Overall, I argue that the reinforcement-based models are in a much better empirical and theoretical position. Hence, transitive inference in non-human animals should be considered a property of reinforcement history rather than of inferential processes. I finalize by shedding some light on some promising lines of research.