The quantum precision measurement method achieves higher accuracy and resolution than conventional measurement methods. Over the past few decades, there is significant progress in the field of quantum-enhanced metrology with respect to the estimation of fixed parameters. However, estimating time-varying parameters is one of the key tasks in numerous practical engineering applications, such as gravitational wave detection, navigation, and positioning. Therefore, designing an effective quantum-enhanced time-varying parameter-estimation method and perfecting the time-varying parameter-estimation theory are important research components related to quantum precision measurement. Recent studies have demonstrated that the accuracy limits of time-varying parameter estimation are closely related to the continuous nature of the signal itself. Moreover, similar to fixed signal measurements, nonclassical sources such as squeezed states can improve the accuracy of time-varying parameter estimation. This review introduces several accuracy limits related to time-varying parameter estimation and summarizes the related research progress.