With the discovery and development of topological materials, topological physics has attracted enormous research interest in the fields of contemporary condensed matter physics. Topological property, which describes such a property that physical quantity remains invariant under continuous transformation (such as Chern number), has been revealed in a variety of materials, including topological insulators, topological semimetals (such as Weyl or Dirac semimetals), topological magnetic materials, etc. One-dimensional chiral magnetic soliton, similar to magnetic skyrmion, is a type of magnetic configuration with topological origin and quasi-particle property, which has shown tremendous physical properties and device functionalities. In this review, we mainly focus on a chiral helimagnet, called Cr_1/3NbS₂, which possesses chiral magnetic soliton lattice and other more spin configurations under different conditions. We systematically summarize the work on Cr_1/3NbS₂, discussing its crystal symmetry, band structure, magnetic interactions, rich magnetic phases, and the physics of associated phase transitions. In particular, the layered crystal structure of Cr_1/3NbS₂ enables us to control the soliton number through tuning the layer number or crystal thickness. Our review provides a comprehensive summary of Cr_1/3NbS₂ in order to draw more attention to this interesting material. Moreover, we envision that our work could offer useful guidance to the researchers working on topological and chiral magnetic materials, and thus introducing topological or chiral magnetism into two-dimensional layered materials and promoting the development of modern magnetism and spintronics. Therefore, this review mainly focuses on a magnet, called Cr_1/3NbS₂. We systematically summarize the work on Cr_1/3NbS₂, discussing its crystal symmetry, band structure, magnetic interaction, rich magnetic phases and the interesting physical phenomena occurring at each phase transition. In addition, the layered crystal structure of Cr_1/3NbS₂ also enables us to use the layer number or crystal thickness to modulate and control its rich magnetic phases. We believe that our review provides a comprehensive summary of Cr_1/3NbS₂, which can make people have a better understanding of a typical topological magnetic material, thereby enriching the material types of magnets and low-dimensional material family and promoting the development of magnetism and spintronics applications, such as in magnetic memory devices, spintronic devices, and quantum information devices.