Although there are several methods for fabricating nanofibrous scaffolds for biomedical applications, electrospinning is probably the most versatile and feasible process. Electrospinning enables the preparation of reproducible, homogeneous fibers from many types of polymers. In addition, implementation of this technique gives the possibility to fabricated polymer-based composite mats embroidered with manifold materials, such as graphene. Flake graphene and its derivatives represent an extremely promising material for imparting new, biomedically relevant properties, functions, and applications. Graphene oxide (GO) and reduced graphene oxide (rGO), among many extraordinary properties, confer antimicrobial properties of the resulting material. Moreover, graphene oxide and reduced graphene oxide promote the desired cellular response. Tissue engineering and regenerative medicine enable advanced treatments to regenerate damaged tissues and organs. This review provides a reliable summary of the recent scientific literature on the fabrication of nanofibers and their further modification with GO/rGO flakes for biomedical applications.