Single crystal fibers (SCF) are considered to be a combination of bulk crystals and conventional fibers, thereby possessing the stable physical and chemical properties accompanied with excellent waveguide properties. This paper gives a detailed introduction to the development history of single crystal fibers, including the evolution of the growth technique and the optimization of the growth process. Laser-heated pedestal growth (LHPG) and Micro-pulling-down (μ-PD) methods are considered to be the most widely used growth techniques for growing single crystal fibers, and the advantages of the two methods are also introduced in detail. The second part of this paper describes the characterization of single crystal fibers, including diameter fluctuation, crystal quality and optical losses. A series of cladding approaches for SCF, such as magnetron sputtering, sol-gel, liquid phase epitaxy, co-drawing LHPG, ion implantation and micro-structure cladding will be reviewed. In addition, the research status of single crystal fiber laser and single crystal fiber sensor are also summarized in view of the current research foundation.