Owing to their favorable properties including small sizes, tight optical confinement, large fractional evanescent fields, and low waveguiding losses, optical micro-/nanofibers have attracted broad research interest and technological applications in recent years, in which the precision in micro-/nanofiber fabrication is critical to determine their waveguiding properties and performances. Here, we firstly introduce the principles of high-temperature taper drawing of glass fibers. Next, we review typical fabrication methods including flame-heated manual drawing approach, flame-heated mechanical drawing technique, electric-heated mechanical drawing technique and laser-heated mechanical drawing technique. Cons and pros of the above-mentioned techniques are discussed, followed by a brief introduction to the fabrication of polymer micro-/nanofibers. Thirdly, we introduce the principle and techniques of high-precision diameter control in glass micro-/nanofiber fabrication based on a