Glass-liquid transition phenomenon, usually known as glass transition, has been valuated as one of the most important challenges in condensed matter physics. As typical amorphous solid, metallic glass is composed of disordered-packing atoms, which is akin to a liquid. Thus, metallic glass is also known as frozen liquid. Metallic glass is an ideal model material for studying glass transition phenomenon. When heated up to glass transition temperature or stressed to yielding point, metallic glass flows. The flow behavior at elevated temperature or under stress plays an important role in the applications of metallic glass. In this paper, we briefly review the research developments and perspectives for the flow behavior and extended elastic model for flow of metallic glasses. In elastic models for flow, i.e., free volume model, cooperative shear transformation model, it is assumed that the activation energy for flow (E) is a combination of shear modulus (G) and a characteristic volume (Vc), E=GVc. Most recently, it has been widely recognized that in amorphous materials, e. g. metallic glass, shear flow is always accompanied by dilatation effect. This suggests that besides shear modulus, bulk modulus (K) should also be taken into account for energy barrier. However, what are the contributions of K is still unknown. On the other hand, the physical meaning of characteristic volume Vc and the determination of its value are also important for quantitatively describing the flow behavior of metallic glass. Based on the statistical analyses of a large number of experimental data, i. e., elastic modulus, glass transition temperature, density and molar volume for 46 kinds of metallic glasses, the linear relationship between RTg/G and Vm is observed. This suggests that the molar volume (Vm) is the characteristic volume involved in the flow activation energy. To determine the contribution of K as a result of shear-dilatation effect, flow activation energy density is defined as E =E/Vm. According to the harmonic analysis of the energy density landscape, we propose that both shear and bulk moduli be involved in flow activation energy density, as E = (1-)G+K, with 9%. This result is also verified by the relationship between elastic modulus and glass transition temperature: (0.91G+ 0.09K)Vm/RTg is a constant, that is, independent of property of metallic glass. This result is also consistent with the evolution of sound velocity with glass transition temperature. In the end of this review, we address some prospects about the applications of the extended elastic model and its significance in designing new metallic glasses with advanced properties. This extended elastic model is also fundamentally helpful for understanding the nature of glass transition and kinetic properties of shear band of metallic glasses.