Organisms must be capable of adapting to environmental task demands. Which cognitive processes best model the ways in which adaptation is achieved? People can behave adaptively, so many frameworks assume, because they can draw from a repertoire of decision strategies, with each strategy particularly fitting to certain environmental demands. In contrast to that multi‐mechanism assumption, competing approaches posit a single decision mechanism. The juxtaposition of such single‐mechanism and multi‐mechanism approaches has fuelled not only much theory‐building, empirical research, and methodological developments, but also many controversies. This special issue on “Strategy Selection: A Theoretical and Methodological Challenge” sheds a spotlight on those developments. The contribution of this introductory article is twofold. First, we offer a documentation of the controversy, including an outline of competing approaches. Second, this special issue and this introductory article represent adversarial collaborations among the three of us: we have modeled adaptive decision making in different ways in the past. Together, we now work on resolving the controversy and point to five guiding principles that might help to improve our models for predicting adaptive behavior. Copyright © 2018 John Wiley & Sons, Ltd.