This paper is focused on the problem as the main tool for modeling of thinking and creativity. It traces the history of using problems in the psychology of thinking and analyzes how classical works in this field describe the relationship between a problem, a task, a problem situation, etc. Problem complexity is treated as the key property that allows researchers to study patterns of the solution process. Two main methods of complexity manipulation are facilitation and inhibition. Each may be external or internal in relation to the problem. Studies of external facilitation look at series of similar problems with a gradual increase in complexity, while internal facilitation involves the reduction of sources of difficulty using a hint. External inhibition studies analyze the role of past experience or social pressure, while internal inhibition entails “reverse hints” that lead the participants away from the correct solution path. This article discusses the following issues: which part of the solution should be complicated to further the theories of problem solving? Can the complication of a problem turn it into a qualitatively more complex problem? Internal problem structure is found to be stable, since all experimental manipulations affect the solution process but leave the essence of the problem intact.