Comparative psychologists study cognition by characterizing the behavior of individual species and explicitly comparing behavior across species. We use the extensive comparative literature on transitive inference (TI) as a case study to evaluate four central methodological questions that continue to be debated in the field of comparative psychology: 1) Are contextual variables sufficient to explain species differences in cognition? 2) Can cognitive performance be accounted for by associative processes alone? 3) Can we determine the cognitive mechanisms by which animals solve tasks? and 4) What is the role of ecologically driven hypotheses in comparative psychology? Although contextual variables and associative processes undeniably influence choice behavior in TI tasks, neither is sufficient to explain all performance. Instead, multiple distinct cognitive mechanisms, including associative processes, logical inference, and spatial representations, can and do result in successful TI performance. TI is not a unitary task solved using a single mechanism; multiple processes are recruited, with their degree of involvement dependent on context, species, and evolutionary pressures. This suggests that rather than asking whether animals possess a certain cognitive ability, research should focus on differences in when and how species employ tools from what is often a reasonably similar cognitive toolbox. We join others who have proposed that a main goal of comparative psychology should be to determine how animals solve cognitive tasks, through minimizing and studying the influence of contextual variables, evaluating the contributions of associative processes, clearly characterizing and testing alternative cognitive mechanisms, and using strong evolutionary hypotheses to guide predictions. (PsycInfo Database Record (c) 2021 APA, all rights reserved).