In the present article, we articulate three assumptions underlying theories proposing that restructuring processes play a key role in insightful problem solving: representational difficulty, representational change, and discontinuity in solution processes. We argue that these assumptions need empirical validation to justify the proposition of restructuring mechanisms that are unique from those involved in classic information-processing theories of problem solving. To this end, we review some theoretical and methodological obstacles that are inherent in the investigation of the existence and nature of restructuring processes. We then offer some recommendations on how to overcome or avoid these obstacles in future studies. Finally, we discuss some questions to help motivate new research.