Logical dynamical systems refer to dynamical systems in which the independent variables take only finite values, including 2-valued classical logic (or Boolean logic), $k $-valued logic, and (generally) mixed-valued logic, and the network topological structure is one of the key factors affecting the performance and reliability of the network. The purpose of this paper is to briefly analyze and summarize the research on the topological structure of logical dynamical systems from several perspectives. First, from the perspective of dynamic evolution, this paper outlines the research methods on attractors in synchronous Boolean networks, asynchronous Boolean networks, and stochastic Boolean networks, which mainly include the simulation method, the BDD technique, the decomposition method, and the feedback vertex set method, etc. Then, from the perspective of structure matrix, this paper summarizes the specific algorithms for solving attractors and basins of attraction in the framework of algebraic state space representation, which demonstrates the superiority of semi-tensor product of matrices in solving topological structure. Finally, from the viewpoint of graphs, this paper briefly summarizes the methods for solving attractors based on wiring diagrams, state transition diagrams, network abridgment, and network partitioning.