Mechanical properties of micro- and nanoscale fibers are superior to their bulk counterparts, and their mechanical behaviors are different from each other. Homogeneous amorphous fibers with smooth surfaces and controllable sizes can be continuously drawn from supercooled liquid. Compared with the preparing of crystalline fibers, the manufacturing of amorphous fibers saves much energy and time. Furthermore, amorphous materials have excellent mechanical properties due to their short-ranged ordered and long-ranged disordered structures. Therefore, amorphous fibers have wide engineering applications and research interest. In this paper we review the fabrication and mechanical behaviors of amorphous fibers with excellent mechanical properties including oxide glass fibers and amorphous alloy fibers.There are continuous and discontinuous oxide glass micro-fibers. Discontinuous oxide glass micro-fibers can be fabricated by techniques in which a thin thread of melt flowing from the bottom of a container is broken into segments. Continuous oxide micro-fibers can be fabricated by techniques in which a filament of supercooled liquid is drawn from melt. However, oxide glass nano-fibers can be fabricated by chemical vapor deposition, laser ablation, sol-gel, and thermal evaporation methods. Fabrication techniques of amorphous alloy fibers are very different from those of oxide glass fibers. These techniques adopt in-rotating-water spinning method, melt-extraction method, Taylor method, nanomoulding method, fast drawing method, melt drawing method, and gas atomization method.Microscale oxide glass fiber has a facture strength as high as 6 GPa. The fracture strength of nanoscale oxide glass fiber can reach 26 GPa which is close to the theoretical strength of 30 GPa. On the other hand, the plasticity of microscale amorphous alloy fibers is mediated by shear banding. The shear band spacing decreases with reducing sample size in bending. However, there is no tensile plasticity in microscale amorphous alloy fibers. When the sample size is smaller than the size of shear band core (500 nm), inhomogeneous plastic deformation transforms into homogeneous plastic deformation. The tensile plasticity of amorphous alloy is significantly improved. The homogeneous plastic deformation is mediated by catalyzed shear transformation. The catalyzed shear transformation may be the origin of hardening behaviors of nanoscale amorphous alloy fibers.Fianlly, we summary the unsolved problems in the fabrications and mechanical behaviors of amorphous fibers, and discuss the prospect of amorphous fibers.