Nanofibers possess high surface area and excellent porosity. Though nanofibers can be produced by a variety of techniques, electrospinning stands distinct because of its simplicity and flexibility in processing different polymer materials, and ability to control fiber diameter, morphology, orientation, and chemical component. Nonetheless, electrospun nanofibers are predominantly produced in the form of randomly oriented fiber webs, which restrict their wide use. Converting nanofibers into twisted continuous bundles, i.e., nanofiber yarns, can improve their strength and facilitate their subsequent processes, but remains challenging to make. Nanofiber yarns also create enormous opportunities to develop well-defined three-dimensional nanofibrous architectures. This review article gives an overview of the state-of-the-art techniques for electrospinning of nanofiber yarns and control of nanofiber alignment. A detailed account on techniques to produce twisted/non-twisted short bundles and continuous yarns are discussed.