Electrospinning is the most versatile and popular technique for preparing nanofibers from a very broad range of polymer systems. In spite of more than 20 years of studies, our understanding of the relationships between the microstructure and the properties of these fibers, and how they are influenced by the electrospinning conditions, remains fragmentary. This is especially true for molecular orientation-a critical parameter that is often invoked to explain the properties of fibers but that is challenging to quantify properly. Recently, the emergence of characterization techniques enabling studies at the,single fiber level, including their orientation, has propelled the field in new directions and provided a wealth of new knowledge. In this Perspective; we review and discuss our current understanding of the structure and properties of electrospun nanofibers with a particular emphasis on their molecular orientation. We first describe how studies at the mat level have provided crucial knowledge about the impact of orientation but also revealed the difficulties associated with its measurement. In the following sections, we present and critically review the most important findings originating from studies of the mechanical and thermal properties of individual fibers. We focus in particular on important models proposed in the literature to explain the variation of the modulus with fiber diameter. We then describe the latest advances in the microstructural characterization of individual fibers. Finally, we show the importance of controlling molecular orientation for some of the most exciting new applications of electrospun nanofibers.