Semiconductor nanowires have demonstrated exciting properties for nanophotonics, sensors, energy technologies, and end-of-roadmap and beyond-roadmap electronic devices. Fabrication schemes for nanowires are varied, but they fall into three general categories: (1) top-down lithographic patterning and etching of bulk crystals and epitaxial films; (2) bottom-up, locally catalyzed crystal growth of nanowires; and (3) hybrid methods that combine aspects of categories (1) and (2). In this article, we examine the relative merits and unique attributes of each of these paradigms for nanowire synthesis. We review literature relevant to nanowire fabrication methods, faceting and dimensional control (diameter and length), positioning and alignment, doping, bulk and surface defects, and formation of unique nanowire heterostructures and metastable phases. Finally, we describe the factors governing selection among top-down, bottom-up, and hybrid methods to fabricate nanowire structures depending on their desired structural features and applications.