Two-dimensional (2D) magnetic materials with magnetic anisotropy can form magnetic order at finite temperature and monolayer limit. Their macroscopic magnetism is closely related to the number of layers and stacking forms, and their magnetic exchange coupling can be regulated by a variety of external fields. These novel properties endow 2D magnetic materials with rich physical connotation and potential application value, which has attracted extensive attention. In this paper, the recent advances in the experiments and theoretical calculations of 2D magnets are reviewed. Firstly, the common magnetic exchange mechanisms in several 2D magnetic materials are introduced. Then, the geometric and electronic structures of some 2D magnets and their magnetic coupling modes are introduced in detail according to their components. Furthermore, we discuss how to regulate the electronic structure and magnetism of 2D magnets by external (external field and interface) and internal (stacking and defect) methods. Then we discuss the potential of using these materials in spintronics devices and magnetic storage. Finally, the difficulties and challenges of 2D magnetic materials and the possible research directions in the future are summarized and prospected.