In physical optics or wave optics, a vector soliton is a solitary wave with multiple components coupled together that maintains its shape during propagation. Ordinary solitons maintain their shape but have effectively only one (scalar) polarization component, while vector solitons have two distinct polarization components. Among all the types of solitons, optical vector solitons draw the most attention due to their wide range of applications, particularly in generating ultrafast pulses and light control technology. Optical vector solitons can be classified into temporal vector solitons and spatial vector solitons. During the propagation of both temporal solitons and spatial solitons, despite being in a medium with birefringence, the orthogonal polarizations can copropagate as one unit without splitting due to the strong cross-phase modulation and coherent energy exchange between the two polarizations of the vector soliton which may induce intensity differences between these two polarizations. Thus vector solitons are no longer linearly polarized but rather elliptically polarized. Definition C.R. Menyuk first derived the nonlinear pulse propagation equation in a single-mode optical fiber (SMF) under weak birefringence. Then, Menyuk described vector solitons as two solitons (more accurately called solitary waves) with orthogonal polarizations which co-propagate together without dispersing their energy and while retaining their shapes. Because of nonlinear interaction among these two polarizations, despite the existence of birefringence between these two polarization modes, they could still adjust their group velocity and be trapped together. Vector solitons can be spatial or temporal, and are formed by two orthogonally polarized components of a single optical field or two fields of different frequencies but the same polarization. History In 1987 Menyuk first derived the nonlinear pulse propagation equation in SMF under weak birefringence. This seminal equation opened up the new field of "scalar" solitons to researchers. His equation concerns the nonlinear interaction (cross-phase modulation and coherent energy exchange) between the two orthogonal polarization components of the vector soliton. Researchers have obtained both analytical and numerical solutions of this equation under weak, moderate and even strong birefringence. In 1988 Christodoulides and Joseph first theoretically predicted a novel form of phase-locked vector soliton in birefringent dispersive media, which is now known as a high-order phase-locked vector soliton in SMFs. It has two orthogonal polarization components with comparable intensity. Despite of the existence of birefringence, these two polarizations could propagate with the same group velocity as they shift their central frequencies. In 2000, Cundiff and Akhmediev found that these two