The GRACE (Gravity Recovery and Climate Experiment) satellite mission, a collaboration between NASA and the German Aerospace Center, was complemented by the launch of its successor, GRACE Follow-On (GRACE-FO), in May 2018. These satellites have crucially contributed to our understanding of Earth's long-term gravitational variations. However, gaps and interruptions in the time-variable gravity field series have arisen due to satellite battery issues, payload calibration errors, and the extended gap between the GRACE and GRACE-FO missions, affecting the continuity and completeness of the data. This paper provides an overview of the GRACE and GRACE-FO missions, data products, and the circumstances of data gaps. It categorizes the reconstruction methods for missing GRACE/GRACE-FO data into two main types: those based on mathematical statistics, the paper focuses on Singular Spectrum Analysis (SSA) and Least Squares Harmonic Analysis (LS-HE), comparing their applicability, strengths, and weaknesses with other methods such as the Autoregressive Moving Average Model (ARMA) and Multi-channel Singular Spectrum Analysis (MSSA). And those using auxiliary information, which employ other satellite data (like GNSS, Swarm, and SLR) and climate and hydrological data, often based on empirical regression relationships or deep learning. This paper evaluates these methods, comparing their applicability, strengths, and limitations, and presents a case study in the Yangtze River Basin using a combination of Empirical Mode Decomposition (EMD) and Long Short-Term Memory (LSTM), showing superior results over methods like Support Vector Machine (SVM), Random Forest (RF), and Iterative Singular Spectrum Analysis (ISSA). In conclusion, while mathematical statistical methods offer simplicity and low computational requirements, deep learning combined with various auxiliary data yields higher quality reconstruction results. In recent years, research both domestically and internationally in this field has also primarily focused on data reconstruction using various deep learning algorithms in conjunction with auxiliary information.The paper contributes to the ongoing research in this field, focusing on deep learning algorithms combined with surface mass models, climate, and hydrological data for data reconstruction, and provides insights for future approaches in filling data gaps for GRACE/GRACE-FO, enhancing the application and research in time-variable satellite gravimetry.