Cooperation is generally defined as involving a group of individuals working together to attain a common goal. In contrast, competition involves one person attempting to outperform another and facilitating the realization of results that benefited to themselves. Cooperation and competition are two key components of social interaction and the two resolutions for conflict. Cooperation contribute to constructive interpersonal relationships while competition may lead to the destructive interpersonal relationships. However, cooperation and competition are important for our daily life, study and business work. In recent years, there are more and more literature to investigate cooperation and competition, however, on the one hand, those focused on human social interaction and the neural mechanism about cooperation and competition is less. On the other hand, fewer researchers investigate cooperation and competition of patients with psychological and psychiatric disorders. The current review summarizes recent researches on cooperation and competition, from the perspective of psychology and society, focused on the neural mechanism, biology basics and the difference between patients’ cooperation and competition, hoping to provide theoretical basis for the rehabilitation training of patients. From the paper, we illuminate the neural mechanism of cooperation and coopetition. Both cooperation and coopetition could result in activation of a common frontoparietal network and the anterior insula. Moreover, distinct regions were found to be selectively associated with cooperation and competition, notably the orbitofrontal cortex in the former and the inferior parietal and medial prefrontal cortices in the latter. We all know that cooperation is divided into reciprocated cooperation and unreciprocated cooperation, unreciprocated cooperation was associated with greater activity in bilateral anterior insula and amygdala compared with reciprocated cooperation. Furthermore, the strength of functional connectivity between anterior insula and lateral orbitofrontal cortex could predicted subsequent defection. When it comes to the biology basics of cooperation and coopetition, researchers argue that oxytocin is associated with cooperation. It, generally speaking, could promote individuals’ cooperative behavior. At the same time, testosterone concentrations are modulated by competition outcome, for example, the testosterone concentrations of winners increases relative to losers in a competitive situation. Besides, changes in testosterone in response to victory or defeat will feedback to influence future dominance-related behaviors. For instance, a rise in testosterone may facilitate competitive behavior, the decrease in testosterone may promote submissive behaviors. In addition, this paper summarizes some researches about the patients’ cooperation and competition, such as anxiety disorders, depressive disorder and personality disorder patients. Besides, these similarities and differences in cooperative and competitive performance are drawn between those patients. We find that diminished cooperativeness may occur in almost all major psychiatric disorders, except to anxiety disorders. However, the tendency to avoid competition only appear in depressive disorder rather than anxiety disorders or personality disorder patients (unpublished data). On the contrary, psychopathy are characteristic of the tendency to compete, suggesting that this abnormality in social behavior may be specific for depressive disorder. Lastly, we try to give some advice on the analysis and research about cooperation and competition, hoping researchers to realize the influence of situation, individual difference and social class, thereby, improving the reliability and generalizability of experimental results.