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 paper, 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. We are living today in the era of nanotechnology. Nanostructures are part of many products, ranging from sunscreens to catalysts to computers. These nanostructures are obtained by very different fabrication methods having aspects of growth from atomic constituents (bottom-up) and/or sculpturing of larger-scale solids down to nanoscale dimensions (top-down). Both top-down and bottom-up approaches have their specific advantages and disadvantages, especially when it comes to semiconductor nanostructures. This situation naturally leads to a question regarding semiconductor nanowires: to grow or not to grow? This review outlines some of the main characteristics of the bottom-up and top-down approaches for nanowire fabrication and of their combination in hybrid methods. Its purpose is to introduce these issues to newcomers to the field and to provide a perspective for deciding on research and development priorities among scientists and engineers investigating semiconductor nanowires and their applications.