Ultrafast fiber lasers have significant applications in laser communications, ultra-precision manufacturing, biomedical diagnostics, and so on. Among all the types of ultrashort pulses, optical vector solitons have attracted significant attention due to their broad range of applications, in particular, in laser sensing and light control technology. Moreover, the research on vector soliton can provide a deeper insight into nonlinear optics and laser physics. In recent years, low-dimensional materials, such as quantum dots, nanowires, graphene, and topological insulator have flourished tremendously, resulting in rapid development of low-dimensional materials-based vector soliton ultrafast fiber lasers. Herein, we reviewed the recent advances on vector soliton in fiber lasers with emerging low-dimensional materials saturable absorber. These low-dimensional materials are classified into 0-dimensional (0D), 1D, 2D, and other new materials. The low-dimensional materials applied in vector soliton generation are emphasized specifically, including material types, unique characteristics, and preparation methods. The recent progress of vector solitons in Yb-, Er-, and Tm-doped fiber laser is also discussed. Finally, the status, challenges, and future directions on this topic are highlighted.