Electrospinning is one of the most important ways to prepare continuous, high porosity, large specific surface area, and uniform diameter micro- and nanoscale fibers. So, it has been widely used in the preparation of micro/nano-sized polymer scaffolds for tissue engineering in recent years. In addition to the versatility in material selection and the processing variables, electrospinning also provides a lot of methods to regulate fiber structure and scaffolds morphology. For example, the near-field electrospinning can provide a method to solve the problem of uncontrollable fiber path; the melt electrospinning eliminates the risk of solvent residue in the construct; the addition of different auxiliary electrodes can make the fiber patterned. This review introduces the underlying principle and characteristics of above electrospinning applied in biomedicine. Herein, we highlight a comprehensive understanding of the technical aspect of this technology for versatile fibers with patterned, core–shell and aligned morphology.