Cellular automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and high computation efficiency. Therefore, CA develops very quickly and has been widely applied in transportation field. In recent two decades, traffic flow study quickly developed, among which 'synchronized flow' is perhaps one of the most important concepts and findings. Many new CA models have been proposed in this direction. This paper makes a review of the development of CA models, concerning their ability to reproduce synchronized flow as well as traffic breakdown from free flow to synchronized flow. Finally, future directions have been discussed.