The present article is devoted to the famous phenomenon in the psychology of creativity, incubation during creative problem solving. Incubation is a break in problem solving, which facilitates efficiency despite the absence of a conscious search. This article introduces a review of the theoretical frameworks and experimental studies of incubation and its cognitive mechanisms. The author describes the main hypotheses about the cognitive mechanisms of the incubation period (such as the forgetting fixation hypothesis, the unconscious work hypothesis, the external cues hypothesis, the attention withdrawal hypothesis), and their empirical evidence. Our theoretical review also contains the main conclusions from meta-analyses, which demonstrate evidence for the incubation effect, and the analysis of the factors affecting the incubation effect size, specifically the type of the main task and the type of the incubation task, the length of the preparatory stage and the length of the incubation phase. Special attention is given to the description of modern neurocognitive studies of creative thinking. These studies aim to investigate the brain systems activated during the incubation period and make it possible to analyze this stage of a creative process in a more detailed way. Incubation is found to be associated with the increased default mode network activity, salience network activity, and activity in motor areas and with the decreased executive attention system activity. In conclusion, the author outlines the conflicting and understudied areas in the theoretical representations of the incubation process that provide prospective directions for future research.