Amorphous solids are metastable materials formed by the rapid quenching of liquid melts. Under mechanical stress, amorphous solid displays unique and complex plastic flow behavior, which is both spatially and temporally inhomogeneous on different length scales. In some cases, the plastic flow behavior of amorphous solid can evolve into the self-organized critical state, which is similar to many complex phenomena in nature and physics such as earthquakes, snow avelanches, motions of magnetic walls, etc. In this paper, we briefly review the recent research progress of the plastic flows of amorphous solids, with an emphasis on the plastic flow of metallic glass which has been one of our research foci in past few years. The review begins with an introduction of the inhomogeneous flow behaviors on different scales, from the macroscopical-scale spatially inhomogeous shear bands, temporally intermittent serrated flow to the atomic-scale localized viscoelastic behavior in metallic glass. The microscopical deformation theories including free volume model and shear transformation zone model, and recent efforts to elucidate macrosopical flow behaviors with these theories, are also presented. Finally, recent progress of the self-organized critical (SOC) behaviors of the plastic flow of metallic glass are reviewed, with an emphasis on its experimental characterizations and the underlying physics. The emergence of SOC in the plastic flow is closely related to the interactions between plastic flow carriers, and based on this point, the relation between the SOC behavior and the plasticity of metallic glass is elucidated. The implications of plastic flow of metallic glass for understanding the occurence of earthquakes are also discussed. The review is also concluded with some perspertives and unsolved issues for the plastic flow of amorphous solids.