The article analyzes explanatory potential of the structural/formal and cognitive models of language as well as coding-encoding, cognitive, inferential, and interactional models of communication to outline alternative explanations of sense making shaped by the models of enacted and situated cognition. It puts forward a conception of communication as an intersubjective interaction in a socially-culturally constructed intersubjective act, initiated by a subject’s focusing attention on a communicative (verbal-coverbal) action of the other subject, which triggers parallel mental processes (involving active perception, affect, cognition, volition, and action) that pass into each other and combine the conscious with the subconscious. Mental structures activated in the act (propositions, images (images-memories as well as images-fantasies; visual and motoric images (patterns of behavior); memories of phrases, gestures, colors, sounds, fragments of melodies, tastes, smells, tactile sensations; inner sensations/anticipations, fragmentary wishes, and moods) self-organize around the subject’s dominant motive to form the current semantic configuration. This dominant motive determines both the intention of the communicative action and the inferences made in the process of interpretation of the communicative action. The article claims that sense making in verbal-coverbal communication does not rest on the conventional nature of a linguistic unit (which all the analyzed models of language and communication eventually appeal to). It rests on the intersubjective nature of human consciousness, a hard-wired capacity of a human social being to share experiential content (thoughts, sensations, emotions, actions), which is being developed in a socially and culturally constructed context of everyday engagements with other social beings.