Traditional electrospinning is a promising technique for fabricating nanofibers for tissue engineering and drug delivery applications. The method is highly efficient in producing nanofibers with morphology and porosity similar to the extracellular matrix. Nonetheless, and in many instances, the process has faced several limitations, including weak mechanical strength, large diameter distributions, and scaling-up difficulties of its fabricated electrospun nanofibers. The constraints of the polymer solution’s intrinsic properties are primarily responsible for these limitations. Reactive electrospinning constitutes a novel and modified electrospinning techniques developed to overcome those challenges and improve the properties of the fabricated fibers intended for various biomedical applications. This review mainly addresses reactive electrospinning techniques, a relatively new approach for making in situ or post-crosslinked nanofibers. It provides an overview of and discusses the recent literature about chemical and photoreactive electrospinning, their various techniques, their biomedical applications, and FDA regulatory aspects related to their approval and marketing. Another aspect highlighted in this review is the use of crosslinking and reactive electrospinning techniques to enhance the fabricated nanofibers’ physicochemical and mechanical properties and make them more biocompatible and tailored for advanced intelligent drug delivery and tissue engineering applications.