Recent studies showed that structural changes in amorphous alloys under high pressure torsion (HPT) are determined by their chemical composition and processing regimes. For example, HPT treatment of some amorphous alloys leads to their nanocrystallization; in other alloys, nanocrystallization was not observed, but structural transformations of the amorphous phase were revealed. HPT processing resulted in its modification by introducing interfaces due to the formation of shear bands. In this case, the alloys after HPT processing remained amorphous, but a cluster-type structure was formed. The origin of the observed changes in the structure and properties of amorphous alloys is associated with the chemical separation and evolution of free volume in the amorphous phase due to the formation of a high density of interfaces as a result of HPT processing. Amorphous metal alloys with a nanocluster structure and nanoscale inhomogeneities, representatives of which are nanoglasses, significantly differ in their physical and mechanical properties from conventional amorphous materials. The results presented in this review show that the severe plastic deformation (SPD) processing can be one of the efficient ways for producing a nanocluster structure and improving the properties of amorphous alloys.