Electrospinning is a method in which materials in solution are formed into nano-and micro-sized continuous fibers. Recent interest in this technique stems from both the topical nature of nanoscale material fabrication and the considerable potential for use of these nanoscale fibres in a range of applications including, amongst others, a range of biomedical applications processes such as drug delivery and the use of scaffolds to provide a framework for tissue regeneration in both soft and hard tissue applications systems. The objectives of this review are to describe the theory behind the technique, examine the effect of changing the process parameters on fiber morphology, and discuss the application and impact of electrospinning on the fields of vascular, neural, bone, cartilage, and tendon/ligament tissue engineering.