Electrospinning is an exciting technique attracting more and more attention as a potential solution to the current challenges in the field of tissue engineering. This technique can be used to produce fibrous scaffolds with excellent biocompatibility and biodegradability, as well as suitable micro-/nanostructure to induce desired cellular activities and to guide tissue regeneration. In order to develop electrospun fibrous scaffolds for these applications, different biocompatible materials including natural polymers, synthetic polymers and inorganic substances and preparations have been used to fabricate electrospun fibers with different structures and morphologies. This review briefly describes the development of the technique, focusing on several typically electrospun materials, surface modification of electrospun fibers, and current applications in tissue engineering.