Abstract This chapter draws a distinction between two types of computational process that mental representations can enter into. Content-specific transitions are transitions between representations that are faithful to representational content due to the specific non-logical concepts involved. Content-general transitions, e.g. deductive inferences, depend only on broadly-logical concepts in order to be faithful to content. Structural representations, which rely on special-purpose compositional principles, tend to enter into content-specific computations rather than broadly-logical inferences. Conceptual representations, relying as they do on general-purpose compositionality, are well suited for content-general computations. However, concepts can also participate in content-specific transitions. The chapter argues that content-specific and content-general computational processes need to be integrated in order to explain concept-driven thinking. The former capture transitions based on pattern recognition and statistical structure, while the latter underpin logical inferences. An account of thinking needs to incorporate both special-purpose and general-purpose inferences involving concepts.