This article first gives a brief review of magnetic structures, magnetic domains and topological magnetic textures and their relations. On the one hand, the magnetic domains are determined by the magnetic structures, the intrinsic magnetic properties and the micro-structural factors of a material. On the other hand, the magnetic domains could control the magnetization and demagnetization processes and also the technical magnetic properties of a material. Topology is found to have a close relation with physical properties of material. Recent interest has focused on topological magnetic textures, such as vortex, bubble, meron, skyrmion, and it has been found that the topological behaviors of these topological textures are closely related with magnetic properties of a material. Then this article introduces recent advances in magnetic structures, magnetic domains and topological magnetic textures, from views of the size effect, defects and interfaces. Finally, this article reviews briefly some results of investigation on the relations between microstructures, magnetic domains and magnetic properties of rare-earth permanent magnetic thin films, the topological magnetic textures and their dynamic behaviors of exchange coupled nanodisks. It has been concluded from the reviews on the literature that the investigation on anisotropic exchange-coupled rare-earth permanent magnets with high performance benefits the high efficient utilization of rare-earth resources. One could achieve optimal magnetic properties through magnetic domain engineering by adjusting the microstructures of magnetic materials. The concepts of topology is applied to various research fields, while the contributions from topological behaviors to physical properties are discovered in different materials. The researches on magnetic domains, topological magnetic ground state and excitation states and their dynamic behaviors are very important for a better understanding of quantum topological phase transitions and other topological relevant phenomena. It can be quite helpful for understanding the correlation between different topological states and their relationship with magnetic properties of a material, and also it will definitely contribute to the applications in various fields of magnetic materials.