Abstract: The long-term accumulated coordinate time series of Global Navigation Satellite System (GNSS) reference stations provide basic data for geodesy and geodynamic studies. Through improving precise GNSS data processing models and strategies, together with investigating physical mechanism and properly modeling of the non-linear variations, the precise position and velocity of GNSS stations can be estimated. This will not only help interpret the plate tectonics reasonably, establish and maintain the terrestrial reference frame, but also contribute to investigating the geodynamic processes, such as post-glacial rebound, sea level change, as well as snow and ice redistribution inversion, et al. In this paper, the basic theory and methodology of GNSS coordinate time series analysis is reviewed by introducing the model estimation of station coordinates time series and the signal analysis. Then, noise modeling technique for GNSS coordinate time series is outlined. Particularly, a rigorous 3-D noise modeling method is proposed to best describe the stochastic process. After that, the advances in investigating physical mechanism of the non-linear variations in GNSS coordinate time series are summarized. Finally, we outline the scientific and engineering applications of GNSS coordinate time series, and discuss the prospect of future research.