Integrating affect in both individual and collective decision-making processes in order to solve real-world problems can be challenging. This research aims to: (1) investigate how group affect (moods, emotions, and feelings) can be integrated and formalized in the decision-making processes; (2) develop current practices; and (3) draw ideas for future perspectives and real-world applications. For this purpose, the role of affect in decision-making is investigated on the individual behavior level, emotional intelligence, and the collective behavior level. The used methodology consists of exploring and investigating the main characteristics developed in group affect in complex decision-making systems from psychology to computer science. From this, a common global structure is deduced: individual processes, group processes and emerging processes (bottom-up, top-down, and combination of bottom-up and top-down components). Following this, one psychological model and two computational models of group emotion and decision are analyzed, and discussed. Their different approaches to developing the main characteristics of a computational model integrating group affect in the decision-making process are highlighted. Finally, specific scenarios of real-world applications are presented in order to draw interesting and promising computational model perspectives.