The increasing progresses in both psychology and computer science allow continually to deal with more and more complex systems and closer to real-world applications in order to solve particularly the decision-making process with uncertain and incomplete information. The aim of this research work is to highlight the irrationality (affect) and to understand some different ways in which the irrationality enter into the decision-making from psychology and computer science perspectives. The goal is also to present some of such integrations of affect in decision-making which emerged in computer science particularly in negotiation and robotics. Thus, the role of the affect in decision-making is developed and discussed. Afterwards, an overview is given on the influence of the affect on an individual level emphasizing the idea that irrationality also has strong social components which can influence the interactions on a group (collective) level. Then, the Emotional Intelligence (EI) is discussed as a first step towards an attempt to answer to how to regulate/control the irrationality part for ‘positive’ decision-making, and consequently its effects on the though and action. Finally, some developments of computational models are presented. Open questions and challenges are discussed in conclusion, particularly the importance of the personality and its links to the affect.