Low-dimensional semiconductor materials structures, where nanowires are needle-like one-dimensional examples, have developed into one of the most intensely studied fields of science and technology. The subarea described in this review is compound semiconductor nanowires, with the materials covered limited to III-V materials (like GaAs, InAs, GaP, InP,...) and III-nitride materials (GaN, InGaN, AlGaN,...). We review the way in which several innovative synthesis methods constitute the basis for the realization of highly controlled nanowires, and we combine this perspective with one of how the different families of nanowires can contribute to applications. One reason for the very intense research in this field is motivated by what they can offer to main-stream semiconductors, by which ultrahigh performing electronic (e.g., transistors) and photonic (e.g., photovoltaics, photodetectors or LEDs) technologies can be merged with silicon and CMOS. Other important aspects, also covered in the review, deals with synthesis methods that can lead to dramatic reduction of cost of fabrication and opportunities for up-scaling to mass production methods.