In this article, we describe a mediational theory of emergent or derived relations resulting from matching-to-sample procedures that produce equivalence and transformation of function. According to a mediational theory, behaviors that occur at the time of reinforcement mediate subsequent behavioral relations referred to as "derived" or "emergent." Such relations have been documented for decades in studies using mostly matching-to-sample procedures with humans and nonhumans. In both verbal human and nonhuman participants, the mediating behaviors consist of differential responding to the sample stimulus. In humans, such behaviors are mostly, but not necessarily, verbal; in nonhumans they include a variety of sample-specific responses, sometimes called "coding." The proposed mediational theory, based only on the four-term contingency and the basic principles of operant learning, makes specific predictions and explains results from a broad range of experiments. There are at least three important implications of a mediational theory. First, if by "derived" or "emergent" one means untrained or unreinforced, then derived relations may not exist. Second, if there are no derived relations, then theories of such relations may not be necessary. Third, a mediational theory of relational responding has potentially important implications for clinical practice.