As the complexity of modern power systems continues to increase, there is a growing need for timely and accurate state monitoring of the distribution grid. Therefore, it is necessary to summarize the existing state estimation methods and explore more reliable ones. This article reviews research on the state estimation of the distribution grid, mainly covering system observability judgment methods, static state estimation methods, and dynamic state estimation methods. First, the article reviews the discernment criteria for system observability in the distribution grid and provides observability judgment methods based on topology and model-based approaches. Next, the paper provides an overview of methods for system static state estimation, introducing orthogonal transformation and the Givens method based on the weighted least squares (WLS) algorithm. It also introduces the maximum likelihood estimation (MLE) used by many power system state estimators as the estimation standard. In addition, the importance of dynamic state estimation (DSE) is discussed, especially when large-scale renewable energy devices and sites are integrated into the generation side. DSE can help grid operators better cope with uncertainties and ensure the reliability of the grid. The article elaborates on methods based on kalman filtering, such as the extended kalman filter (EKF) and the uncertain kalman filter (UKF), which have been widely used in DSE. Finally, against the backdrop of the rise of deep learning technology, this article expands on some researchers' attempts to integrate data-driven algorithms into state estimation research.