In this talk, I will report some recent advances in the understanding of recurrence properties, their applications to quantify the dynamics of the underlying systems, and the interrelationship with the research line of complex network. In particular, I show an example of complex network from climate system; reconstruction of complex networks driven by large scale data sets; identification of the correct coupling directions; characterization of structural properties of time series from complex network perspective. It is demonstrated that there are fundamental relationships between many topological properties of the network and different non-trivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the network) related with the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis. Finally, I will propose to use measures of complex networks to identify dynamical transitions including both modeled systems and the real time series. Some particular interesting complex periodic windows are identified by our methods.