The article is dedicated to the insight phenomenon, namely the explanations of the rela-tionship between cognitive and affective components of insight that different theories suggest. The affective component of insight includes the subjective suddenness, certainty, and pleasure with which the solution comes to mind (Aha! experience). The cognitive component of insight is the assumed mechanisms contributing to the generation of the solution. In the first part of the article, we review classical approaches to explain the insight phenomenon's nature: special processes account and business-as-usual account. In the first approach, two mecha-nisms can be suggested: unconscious associative processing and representational change (restructuring). According to the business-as-usual account, insight solutions do not differ from routine ones and are implemented as a step-by-step movement to the goal state. In the second part of the article, we show that all classical theories of insight problem solving suggest the direct relation between Aha! experience and cognitive mechanisms of insight. Then, we analyze accumulated empirical data that stand for or against this notion. Based on this analysis, we conclude that there is no unequivocal evidence for the direct rela-tion between Aha! experience and the unconscious processing or restructuring. We propose that Aha! experience is an anomaly for the studies of insight problem-solving. The third part of the article aims to review possible ways to resolve the problem of Aha! experience. One way is to consider that the relation between affective and cognitive compo-nents of insight is indirect. We review studies of metacognition where the non-specificity of metacognitive experiences was proposed. According to this idea, metacognitive experiences reflect changes in cognitive processes dynamics (such as the information processing fluency) but do not carry specific information about their source. In the fourth part of the article, the attempts to apply the idea of non-specificity to the Aha! experience are reviewed. We analyze the empirical data supporting the hypothesis of indirect relation between Aha! experience and cognitive mechanisms of insight problem-solving. Based on it, we predict an increase in the number of studies developing this idea.