Nanofibers have been the subject of recent intensive research due to their unique properties, especially their large surface-area-to-volume ratio, which is about 1000 times higher than that of a human hair. They also have several other remarkable characteristics, such as flexibility in surface functionality, superior mechanical properties such as stiffness and tensile strength, their capacity to be formed into a variety of shapes, and the fact that they can be produced from a wide range of organic and inorganic polymers and ceramics. These outstanding properties make polymer nanofibers the optimal candidates for providing significant improvements in current technology and for opening the door to novel applications in many research areas. The present review presents a comprehensive summary of the existing solution and melts electrospinning technologies and the effects of parameters on the electrospinning process and nanofiber morphology.