Collective behavior in complex networks is an important topic of interdisciplinary study. Ethology has shown the ubiquity of collective behavior, and has proven the rationality of evolutionary theory in explaining the emergence of collective behavior. Evolutionary game theory in complex network has obtained substantial developments, especially in quantitative analysis of two-strategy competition. In this paper, the mechanisms for the evolution of cooperation are given under the framework of evolutionary game, and the effects of individual heterogeneity and environmental feedback on cooperation have attracted growing interests. Second, five main theoretical methods have been addressed for analyzing the evolutionary game in complex networks, including the coalescing random walk theory for any network structure and update rule, which is recently proposed. Then, the studies on the evolution of fairness in ultimatum games are presented. Finally, the challenges and further directions of studying ultimatum games in complex network have been summarized.