Abstract: Topological quantum states have become one of the most frontline topics in condensed matter physics since the 21st century. They have not only deepened our understanding of the states of matter, but also hold great promise for future potential applications. Although there has been a well-established framework for nonmagnetic topological states, the study of magnetic topological states is still in its infancy. In the last two years, the discovery of the MnBi<sub<2</sub<Te<sub<4</sub< family of intrinsic magnetic materials has given rise to an upsurge of studies on magnetic topological insulators. Here, starting from basic principles, we give a brief introduction to important advances in this field. Antiferromagnetic topological insulators, axion insulators, and dynamical axion insulators in the MnBi<sub<2</sub<Te<sub<4</sub< family are extensively discussed. Finally, we present a simple perspective on magnetic topological states.