Topological state is a rapidly emerging branch of condensed matter physics in recent years, among which two-dimensional topological insulators (2D TIs) have attracted wide attentions due to their great potential in basic research and applications. The 2D TI has insulating bulk state and conductive edge state. Its edge state is protected by time inversion symmetry and will not be backscattered by weak disordered impurities on the boundaries, thus forming a dissipationless edge conductive channel. Compared with 3D TIs, the edge state of 2D TIs can only propagate in two directions, meaning stronger anti-interference with robustness, thus is of great significance for the development of advanced integrated circuits with low energy consumption. Among many experimental methods for studying two-dimensional materials, scanning tunneling microscopy is a surface-sensitive tool with high atomic and energy resolution to locally detect the electronic structure of the material surface. By detecting the edge state of 2D materials in real space, it is particularly suitable for characterizing their topological properties. This paper traces the research progress of 2D TIs, and illustrates their spectroscopic evidences to resolve the nontrivial properties of the one-dimensional edge states. Combined with theoretical calculations, the topological edge states are verified to reside within the bulk energy gap, as well as being localized in the vicinity of step boundaries with a specific spatial distribution in real space. Finally, we discuss the tunability and manipulations of 2D topological materials through structural and external fields, which show promising prospects for applications in future spintronics and energy-saving devices.