Conscious and unconscious brain mechanisms, including cognition, emotions and language are considered in this review. The fundamental mechanisms of cognition include interactions between bottom-up and top-down signals. The modeling of these interactions since the 1960s is briefly reviewed, analyzing the ubiquitous difficulty: incomputable combinatorial complexity (CC). Fundamental reasons for CC are related to the Gödel’s difficulties of logic, a most fundamental mathematical result of the 20th century. Many scientists still “believed” in logic because, as the review discusses, logic is related to consciousness; non-logical processes in the brain are unconscious. CC difficulty is overcome in the brain by processes “from vague-unconscious to crisp-conscious” (representations, plans, models, concepts). These processes are modeled by dynamic logic, evolving from vague and unconscious representations toward crisp and conscious thoughts. We discuss experimental proofs and relate dynamic logic to simulators of the perceptual symbol system. “From vague to crisp” explains interactions between cognition and language. Language is mostly conscious, whereas cognition is only rarely so; this clarifies much about the mind that might seem mysterious. All of the above involve emotions of a special kind, aesthetic emotions related to knowledge and to cognitive dissonances. Cognition-language-emotional mechanisms operate throughout the hierarchy of the mind and create all higher mental abilities. The review discusses cognitive functions of the beautiful, sublime, music.