Fiber structures with nanoscale diameters offer many fascinating features, such as excellent mechanical properties and high specific surface areas, making them attractive for many applications. Among a variety of technologies for preparing nanofibers, electrospinning is rapidly evolving into a simple process, which is capable of forming diverse morphologies due to its flexibility, functionality, and simplicity. In such review, more emphasis is put on the construction of polymer nanofiber structures and their potential applications. Other issues of electrospinning device, mechanism, and prospects, are also discussed. Specifically, by carefully regulating the operating condition, modifying needle device, optimizing properties of the polymer solutions, some unique structures of core–shell, side-by-side, multilayer, hollow interior, and high porosity can be obtained. Taken together, these well-organized polymer nanofibers can be of great interest in biomedicine, nutrition, bioengineering, pharmaceutics, and healthcare applications.