Small bodies like asteroids and comets are little differentiated objects that have preserved information about the early state of our solar system. Depending on the heliocentric distance of their origin and their further development they exhibit different pristine compositions that include minerals, ices, and refractory organics. Thus, the composition analysis of minor bodies enables investigations of their evolutionary paths and insights into early processes of planetary formation. In the last decades, new spaceflight and instrument technologies enabled detailed investigations of such bodies during flybys, orbital observations, in situ studies with descent probes, and lander experiments. Core payload elements of these missions include VIS to IR spectrometers, which provided regional and global maps of surface composition, texture, and temperature. The wide range of materials to be detected and the large variability of measurement conditions require dedicated instrumentation and observation strategies for this purpose. This paper reviews the state of the art knowledge and technology achievements in this research field. Scientific results, requirements, and instrumental solutions for minor planetary body studies with VIS to IR spectrometers and radiometers are discussed using examples like the Rosetta mission to comet 67P/Churyumov-Gerasimenko, the asteroid missions Dawn to 4 Vesta and 1 Ceres (dwarf planet), and Hayabusa2 to 162173 Ryugu. Based on our present knowledge, open questions in minor body research are summarized, and resulting scientific and instrumental requirements for future spaceborne VIS/IR spectral studies are elaborated in detail.