This paper argues that conversation analysis has largely neglected the fact that meaning in interaction relies on inferences to a high degree. Participants treat each other as cognitive agents, who imply and infer meanings, which are often consequential for interactional progression. Based on the study of audio- and video-recordings from German talk-in-interaction, the paper argues that inferences matter to social interaction in at least three ways. They can be explicitly formulated; they can be (conventionally) indexed, but not formulated; or they may be neither indexed nor formulated yet would be needed for the correct understanding of a turn. The last variety of inferences usually remain tacit, but are needed for smooth interactional progression. Inferences in this case become an observable discursive phenomenon if misunderstandings are treated by the explication of correct (accepted) and wrong (unaccepted) inferences. The understanding of referential terms, analepsis, and ellipsis regularly rely on inferences. Formulations, third-position repairs, and fourth-position explications of erroneous inferences are practices of explicating inferences. There are conventional linguistic means like discourse markers, connectives, and response particles that index specific kinds of inferences. These practices belong to a larger class of inferential practices, which play an important role for indexing and accomplishing intersubjectivity in talk in interaction.