Collective behaviorsare important emergent phenomena in complex systems, from whichmacroscopic spatiotemporal or functional structure will emerge viainteractions between microscopic individuals. Previous studiesindicated that the structure of complex network related with theinteraction between individuals had important effects oncollective behaviors in complex systems. Based on the researcheson Ising model of complex networks, recent studies on collectivebehaviors on complex networks are reviewed in this article. First,the critical phenomena emerged in Ising model is presented as wellas the effects of network's structure on phase transition. Second,efforts are focused on the application of Ising model to socialand economic systems, including opinion formation, herd behaviorand segregation phenomenon, with emphasis laid on the effects ofnetwork's structure on collective behaviors. Thirdly, theapproaches to detect community structure of networks based onIsing model are presented, and finally discussions and concludingremarks are given.