Fiber laser is a perfect platform to generate and study the scalar and vector optical solitons. The optical solitons formation in fiber lasers is a result of the mutual interaction among the cavity dispersion, fiber nonlinearity, laser gain saturation and gain bandwidth filtering. Solitons in fiber lasers have been obtained by passive mode locking of the lasers that could be achieved by inserting a saturable absorber into the laser cavity. Graphene as a promising saturable absorber that has super broad operation bandwidth was proposed to use in the fiber lasers to generate vector solitons, which opened the study of vector solitons in the mode-locked fiber lasers. In the current dissertation, the author presents a series of investigations on the bright-bright vector solitons formed in fiber lasers mode locked with graphene. Novel types of soliton generation including scalar dark soltions and vector dark-bright solitons in the non-mode-locking fiber lasers were also experimentally investigated and presented.