We propose a phenomenological theory to model shear banding, shear-band propagation and branching on mesoscopic scales in metallic glasses by using Ginzburg-Landau formulism. The disordering caused by mechanical or thermal agitation is represented by atomic volume dilatation and used as an order parameter. This model captures several important features in the deformation process, namely, shear localization or banding, shear-band propagation and branching, and crack propagation and its velocity. We also assessed the relation between the crack propagation velocity and local heating and the connection between the serrated flow and shear band branching. DOI: 10.1103/PhysRevB.80.104201 PACS number͑s͒: 62.25.Mn, 46.50.ϩa, 61.43.Bn, 61.43.Fs One of the most promising developments in metallic materials in recent years is the invention of bulk metallic glasses ͑BMGs͒. 1,2 BMGs are topologically disordered solids without the long-range translational order as seen in crystalline materials. The disordered structure with atoms packed randomly leads to many unique and outstanding properties. Perhaps the most interesting is the phenomenon called shear localization: when a metallic glass subject to external load reaches the flow stress, plastic deformation occurs in narrow bands. The deformation strain inside the band is many times larger than that outside, causing samples to fail locally and quickly. The shear localization is by far identified as the only mechanism that affects the strength, ductility, and thus application of the BMGs which otherwise have many potential applications derived from the superb properties. 1-4 Shear banding consists of three stages: nucleation, growth and propagation, and final failure; and each stage occurs on a different spatial and temporal scale. Shear-band nucleation occurs in less than microsecond and with the critical nucleation size of about 10 to several hundred nanometers, depending on the material and ambient conditions. 1-5 Once the critical state is approached, the band could grow and propagate; the bands grow into steady state, or maturity with typical thickness of tens of nanometers to hundreds of nanometers and length of many times larger than the thickness, depending on the propagation condition. 1-5 A propagating shear band often becomes unstable, resulting in branching into subbands. [1][2][3][4][5] The mechanical properties of metallic glasses are determined by the detailed behavior of the shearband evolution. For example, a shear band starting propagating would affect yielding, or strength, and its propagation and branching would contribute to ductility as more deformation is concentrated inside the bands, absorbing more deformation energy and thus contributing to higher toughness. In addition, as we identify below, shear-band branching may be a major reason for the serrated flow observed during plastic deformation.The evolution exhibited in a localized shear band is a complex interplay of many factors. The initiation of a shear band is related to the local stress concentra...