Evolutionary games on complex networks are considered in this paper. First, the evolutionary Prisoner's dilemma game on scale-free networks with community structures is investigated. Then the heterogeneity's role in the evolution of cooperation on a variant of Newman-Watts small-world networks is explored. The influence of different initial conditions on the evolution of cooperation corresponding to different initial configurations for cooperators and defectors distributing among the vertices of networks is also studied. Moreover, Snowdrift game on an empirical social network is considered, and the entangled dynamics of the evolution of network structure and strategy is investigated. The reinforcement learning dynamics in networked populations playing Prisoner's dilemma is also explored. Finally, some open problems, future research directions, and possible application areas of evolutionary games on complex networks are presented.