The interaction between non-trivial topological states and the magnetic order of intrinsic magnetic topological insulators gives rise to various exotic physical properties, including the quantum anomalous Hall effect and axion insulator. These materials possess great potential applications in low-power topological spintronic devices and topological quantum computation. Since the first intrinsic magnetic topological insulator, MnBi₂Te₄, was discovered in 2019, this material system has received significant attention from researchers and sparked a research boom. This paper begins with discussing the fundamental properties of MnBi₂Te₄ and then turns to important research findings related to this intrinsic magnetic topological insulator. Specifically, it focuses on the quantum anomalous Hall effect, axion insulating state, and Majorana zero energy mode exhibited by the MnBi₂Te₄ series. Furthermore, this paper highlights other research directions and current challenges associated with this material system. Finally, this paper provides a summary and outlook for future research on MnBi₂Te₄, aiming to offer valuable references for researchers in related fields.