Advancements in technology and material development in recent years has led to significant breakthroughs in the remit of fiber engineering. Conventional methods such as wet spinning, melt spinning, phase separation and template synthesis have been reported to develop fibrous structures for an array of applications. However, these methods have limitations with respect to processing conditions (e.g. high processing temperatures, shear stresses) and production (e.g. non-continuous fibers). The materials that can be processed using these methods are also limited, deterring their use in practical applications. Producing fibrous structures on a nanometer scale, in sync with the advancements in nanotechnology is another challenge met by these conventional methods. In this review we aim to present a brief overview of conventional methods of fiber fabrication and focus on the emerging fiber engineering techniques namely electrospinning, centrifugal spinning and pressurised gyration. This review will discuss the fundamental principles and factors governing each fabrication method and converge on the applications of the resulting spun fibers; specifically, in the drug delivery remit and in regenerative medicine.