In this paper, a history of development of bulk metallic glasses (BMGs) was presented, followed by a review of fundamental mechanisms of their deformation and fracture. In this study, observations of fracture surfaces of the Zr-Cubased BMG exposed to a 3-point test revealed features that are different from those observed in crystalline materials. Indentation techniques were extensively used to characterise elastic deformation of the studied BMG alloy, followed by a systematic analysis of initiation and evolution of shear-band localisation in the indented material. Our results, obtained with the suggested wedge-indentation technique, demonstrated initiation of shear bands in the material volume. This technique can be particularly useful for development of appropriate constitutive models to analyse plastic events in amorphous materials in the small-length scale. A current state of constitutive models of deformation and fracture behaviour of BMGs are presented together with modelling challenges. Simulation of simple tensile and compressive tests were conducted with JH-2, JHB and Drucker-Prager constitutive models by employing identical boundary conditions, type of element and specimen's geometry. Based on the obtained simulation results, the JH-2 model was considered as not suitable for quasi-static analysis due to ambiguity of the data produced with it for uniaxial tensile and compressive conditions. However, it is concluded that the extended Drucker-Prager and JHB models can be used to study deformation modes in BMGs.