Early diagnosis and efficient treatment are of paramount importance to fight cancers. Monitoring the foreign body response of a patient to treatment therapies also plays an important role in improving the care that cancer patients receive by their medical practitioners. As such, there is extensive research being conducted into ultrasensitive point-of-care detection systems and "smart" personalized anti-cancer drug delivery systems. Electrospun nanofibers have emerged as promising materials for the construction of nanoscale biosensors and therapeutic platforms due to their large surface areas, controllable surface conformation, good surface modification, complex pore structure, and high biocompatibility. Electrospun nanofibers are produced by electrospinning, which is a very powerful and economically viable method of synthesizing versatile and scalable assemblies from a wide array of raw materials. This review describes the theory of electrospinning, achievements, and problems currently faced in producing effective biosensors/drug delivery systems, in particular, for cancer diagnosis and treatment. Finally, insights into future prospects are discussed.