Amorphous alloys (also known as metallic glasses) exhibits excellent catalytic, soft magnetic, magnetocaloric and mechanical properties. Their far-from-equilibrium nature bestow amorphous alloys some special characteristics that are different from crystalline materials, such as glass transition, disordered atomic packing structure, and atomic relaxations. It has been a long-standing pursuit to explore the correlations between the functional properties and amorphous characteristics for amorphous alloys. A deep understanding of the underlying science for the correlations can help improving the functional properties of amorphous alloys and promote their applications.