The most important applications of electrospun polymeric nanofibers are by far those from biomedical field. From the biological point of view, almost all the human tissues and organs consist of nanofibroas structures. The examples include the bone, dentine, cartilage, tendons and skin. All these are characterized through different fibrous structures, hierarchically organized at nanometer scale. Electrospinning represents one of the nanotechnologies that permit to obtain such structures for cell cultures, besides other technologies, such as selfassembling and phase separation technologies. The basic materials used to produce electrospun nanofibers can be natural or synthetic, having polymeric, ceramic or composite nature. These materials are selected depending of the nature and structure of the tissue meant to be regenerated, namely: for the regeneration of smooth tissues regeneration one needs to process through electrospinning polymeric basic materials, while in order to obtain the supports for the regeneration of hard tissues one must mainly use ceramic materials or composite structures that permit imbedding the bioactive substances in distinctive zones of the matrix. This work presents recent studies concerning basic materials used to obtain electrospun polymeric nanofibers, and real possibilities to produce and implement these nanofibers in medical bioengineering applications.