interactions, the bound vector solitons could have much stronger interaction forces than can exist between scalar solitons. Vector dark soliton Dark solitons are characterized by being formed from a localized reduction of intensity compared to a more intense continuous wave background. Scalar dark solitons (linearly polarized dark solitons) can be formed in all normal dispersion fiber lasers mode-locked by the nonlinear polarization rotation method and can be rather stable. Vector dark solitons are much less stable due to the cross-interaction between the two polarization components. Therefore, it is interesting to investigate how the polarization state of these two polarization components evolves. In 2009, the first dark soliton fiber laser has been successfully achieved in an all-normal dispersion erbium-doped fiber laser with a polarizer in cavity. Experimentally finding that apart from the bright pulse emission, under appropriate conditions the fiber laser could also emit single or multiple dark pulses. Based on numerical simulations we interpret the dark pulse formation in the laser as a result of dark soliton shaping. Vector dark bright soliton A "bright soliton" is characterized as a localized intensity peak above a continuous wave (CW) background while a dark soliton is featured as a localized intensity dip below a continuous wave (CW) background. "Vector dark bright soliton" means that one polarization state is a bright soliton while the other polarization is a dark soliton. Vector dark bright solitons have been reported in incoherently coupled spatial DBVSs in a self-defocusing medium and matter-wave DBVS in two-species condensates with repulsive scattering interactions, but never verified in the field of optical fiber. Induced vector soliton Using a birefringent cavity fiber laser, an induced vector soliton may be formed due to the cross-coupling between the two orthogonal polarization components. If a strong soliton is formed along one principal polarization axis, then a weak soliton will be induced along the orthogonal polarization axis. The intensity of the weak component in an induced vector soliton may be so weak that by itself it could not form a soliton in the SPM. The characteristics of this type of soliton have been modeled numerically and confirmed by experiment. Vector dissipative soliton A vector dissipative soliton could be formed in a laser cavity with net positive dispersion, and its formation mechanism is a natural result of the mutual nonlinear interaction among the normal cavity dispersion, cavity fiber nonlinear Kerr effect, laser gain saturation and gain bandwidth filtering.