Electrospinning represents a simple and effective strategy for fabricating nanofibrous structures and materials with large surface-to-volume ratios and desirable engineered properties. Thus, incorporating nanoscale building blocks (NBBs) like nanoparticles, graphene quantum dots, carbon nanotubes, and graphene into electrospun fibers has become one of the most attention-getting research topics in the field of biosensing. However, the dispersion behavior of NBBs in the nanofibers, the limited surface area of nanofibers and the insufficient immobilization sites for tested biomolecules still restrict the better performances and broader applications of the fabricated biosensors. In this review, we present a comprehensive survey of strategies that have been utilized to fabricate functional fibrous nanostructures for the amplification of the detection signals of nanostructure-based biosensors. In particular, from the perspective of design configuration, we systematically summarized recent advances in the electrospinning fabrication of hybrid polymer nanofibers decorated with functionalized NBBs. The strategies for promoting better dispersion of NBBs in electrospun nanofibers, including direct blending before electrospinning and in situ synthesis during electrospinning, are introduced in detail. In addition, some effective processing routes for increasing immobilization sites of tested biomolecules such as arrangement of NBBs and morphological processing of nanofibers are also presented. In addition, the suitability of electrospun nanostructures for biosensors, and the advantages and disadvantages of each method for improving the biosensing performance are also discussed.