Electrospinning (ES) is a convenient and versatile method for the fabrication of nanofibers and has been utilized in many fields including pharmaceutical and biomedical applications. Conventional ES uses a needle spinneret for the generation of nanofibers and is associated with many limitations and drawbacks (i.e., needle clogging, limited production capacity, and low yield). Needleless electrospinning (NLES) has been proposed to overcome these problems. Within the last two decades (2004-2020), many research articles have been published reporting the use of NLES for the fabrication of polymeric nanofibers intended for drug delivery and biomedical tissue engineering applications. The objective of the present mini-review article is to elucidate the potential of NLES for designing such novel nanofibrous drug delivery systems and tissue engineering constructs. This paper also gives an overview of the key NLES approaches, including the most recently introduced NLES method: ultrasound-enhanced electrospinning (USES). The technologies underlying NLES systems and an evaluation of electrospun nanofibers are presented. Even though NLES is a promising approach for the industrial production of nanofibers, it is a multivariate process, and more research work is needed to elucidate its full potential and limitations.