Electrospinning is a versatile process technology, exploited for the production of fibers with varying diameters, ranging from nano- to micro-scale, particularly useful for a wide range of applications. Among these, tissue engineering is particularly relevant to this technology since electrospun fibers offer topological structure features similar to the native extracellular matrix, thus providing an excellent environment for the growth of cells and tissues. Recently, nanocarbons have been emerging as promising fillers for biopolymeric nanofibrous scaffolds. In fact, they offer interesting physicochemical properties due to their small size, large surface area, high electrical conductivity and ability to interface/interact with the cells/tissues. Nevertheless, their biocompatibility is currently under debate and strictly correlated to their surface characteristics, in terms of chemical composition, hydrophilicity and roughness. Among the several nanofibrous scaffolds prepared by electrospinning, biopolymer/nanocarbons systems exhibit huge potential applications, since they combine the features of the matrix with those determined by the nanocarbons, such as conductivity and improved bioactivity. Furthermore, combining nanocarbons and electrospinning allows designing structures with engineered patterns at both nano- and microscale level. This article presents a comprehensive review of various types of electrospun polymer-nanocarbon currently used for tissue engineering applications. Furthermore, the differences among graphene, carbon nanotubes, nanodiamonds and fullerenes and their effect on the ultimate properties of the polymer-based nanofibrous scaffolds is elucidated and critically reviewed.