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Many studies have been conducted on the role of constraints in psychology and artificial intelligence (AI) since the 1960s. In psychology as well as in AI, these studies were carried out in various problem-solving domains, such as design or scheduling, and involved cooperative or individual problem-solving. Although many definitions and approaches to constraints have been suggested, no synthesis article has been forthcoming. This is the purpose of this paper. This paper reviews cognitive and ergonomic psychology research that seeks to tackle the issue of constraints. Included in this review are the main studies taken from AI and used in psychology. As most studies have focused on the role of constraints in individual problem-solving situations, we chose to attend more precisely to these activities and to illustrate them with various examples taken from empirical studies. Our review starts with the presentation of the main definitions, typologies, and statuses often attributed to constraints in psychology and AI. Looking beyond the controversy surrounding these, we highlight how they may be complementary to each other. The second part of this review introduces the operations based on constraints, emphasizing the three operations found within AI and psychology: formulation, propagation and satisfaction. We define these operations according to the AI approach, and emphasize their psychological implications. Then, we present the two most frequently studied operations in psychology: relaxation and the elimination of constraints. Finally, this paper suggests three ways of carrying out research into the role of constraints in problem-solving, focusing on: 1 / relationships between constraints and complexity, 2 / relationships between constraints and difficulty, and 3 / relationships between constraints and attention processes.