Electrospinning is a promising method for producing polymer materials composed of micro- and nanosized fibers. This method allows the preparation of random and aligned fibers of different morphologies, such as cylindrical or ribbon-shapes, defect-free or with defects, and with or without pores or porous. The increasing number of studies on electrospinning requires a set of criteria for more complex evaluation of the fiber morphology and the topology of these polymer materials to be established. The main characteristics necessary for a complex evaluation of the morphology of electrospun micro- and nanofibers have been systematized in this paper. Examples of characterization of the morphology and of the alignment of various micro- and nanofibers are given.