Finite-difference (FD) method is the most extensively employed numerical modeling technique. Nevertheless, when using the FD method to simulate the seismic wave propagation, the large spatial or temporal sampling interval can lead to dispersion errors and numerical instability. In the FD scheme, the key factor in determining both dispersion errors and stability is the selection of the FD weights. Thus, How to obtain appropriate FD weights to guarantee a stable numerical modeling process with minimum dispersion error is critical. The FD weights computation strategies can be classified into three types based on different computational ideologies, window function strategy, optimization strategy, and Taylor expansion strategy. In this paper, we provide a comprehensive overview of these three strategies by presenting their fundamental theories. We conduct a set of comparative analyses of their strengths and weaknesses through various analysis tests and numerical modelings. According to these comparisons, we provide two potential research directions of this field: Firstly, the development of a computational strategy for FD weights that enhances stability; Secondly, obtaining FD weights that exhibit a wide bandwidth while minimizing dispersion errors.