The proposal and development of optical topological edge states have opened up a new direction for solving the problem that traditional photonic devices are vulnerable to impurity interference, which can significantly enhance the robustness of electromagnetic wave propagation and is of great significance for the design of new photonic devices. As a metamaterial, plasma can effectively control the propagation of electromagnetic waves. Its hyperbolic dispersion characteristics, negative permittivity and time-varying characteristics create advantages for exploring novel plasma topological phases, and are expected to promote the development of black barrier electromagnetic communication technology, tunable microwave devices and photonic time crystals. Based on the development process of plasma photonic crystals, the generation methods of plasma arrays, such as dielectric barrier discharge, plasma jet, glow discharge, etc., are briefly reviewed, and the characteristics such as nonlinear Kerr effect, flat-band localized mode, non-reciprocal propagation in magnetized plasma are discussed. The development process and research status of topological phases in plasma are further reviewed in detail, and the schemes for realizing topological edge states by means of solid-state semiconductor materials, gas discharge plasma, dielectric-plasma composite structures are introduced. Finally, the development status, advantages and challenges of the topological characteristics of discharge plasma are summarized and prospected.