Most, if not all, languages exhibit “animacy effects”: grammatical structures interact with the relative animacy of noun referents, as represented on various versions of animacy scales, with human discourse participants at one end and inanimate objects at the other. Cross-linguistic evidence attests to a range of linguistic phenomena conditioned by animacy, with complex effects requiring (a) subtler distinctions than a binary contrast [± animate] and (b) more sophisticated analyses than mapping higher animacy to higher grammatical role. This paper introduces the Special Issue, “Effects of Animacy in Grammar and Cognition”, in which the linguistic interest in grammatical effects of animacy is aligned with broader questions concerning animacy in cognition, including the origins of animacy in language, the biases underlying how we attend to animacy distinctions and how animacy affects discourse. Recent work in cognitive science and adjacent fields has contributed to the understanding of the role of animacy across linguistic domains. Yet, despite the consensus that sensitivity to animacy is a property central to human cognition, there is no agreement on how to incorporate animacy within linguistic theories. This SI focusses on the cognitive construal of animacy, aiming to extend our understanding of its role in grammar(s) and theory.