As an Introduction to the Special Issue on "Formulation, generalization, and abstraction in interaction," this paper discusses key problems of a conversation analytic (CA) approach to semantics in interaction. Prior research in CA and Interactional Linguistics has only rarely dealt with issues of linguistic meaning in interaction. It is argued that this is a consequence of limitations of sequential analysis to capture meaning in interaction. While sequential analysis remains the encompassing methodological framework, it is suggested that it needs to be complemented by analyzing semantic relationships between choices of formulation in the interaction, ethnography, and structural techniques of comparing selected options with possible alternatives. The paper describes the methodological approach taken to interactional semantics by the papers in the Special Issue, which analyse practices of generalization and abstraction in interaction as they are accomplished by formulations of prior versions of reference and description.