Asteroids and other Small Solar System Bodies (SSSBs) are of high general and scientific interest in many aspects. The origin, formation, and evolution of our Solar System (and other planetary systems) can be better understood by analysing the constitution and physical properties of small bodies in the Solar System. Currently, two space missions (Hayabusa 2, OSIRIS-REx) are on their way to their respective targets and perform samples return; other missions have been selected or proposed to space agencies. The threat posed to our planet by Near- Earth Objects (NEOs) is also considered at the international level, and this has prompted dedicated research on possible mitigation techniques. Thus, the DART space mission will test the kinetic impact technique. Even ideas for industrial exploitation have risen during the last years, as future space mission projects will undoubtedly target some asteroids or other SSSBs. Lastly, the origin of water and life on Earth appears to be connected to asteroids. In all these cases and research topics, specific knowledge of the structure and mechanical behaviour of the surface as well as the bulk of those celestial bodies is crucial. In contrast to large telluric planets and dwarf planets, a large proportion of such small bodies is believed to consist of gravitational aggregates (‘rubble piles’) with no—or low—internal cohesion, with varying macro-porosity and surface properties (from smooth regolith covered terrain, to very rough collection of boulders), and varying topography (cratering, depressions, ridges). Bodies with such structure can sustain some plastic deformation without being disrupted in contrast to the classical visco-elastic models that are generally valid for planets, dwarf planets, and large satellites. These SSSBs are hence better approached through granular mechanics theories, which have been a subject of intense theoretical, experimental, and numerical research over the last four decades. This being the case, it has been necessary to use the theoretical, numerical and experimental tools developed within Soil Mechanics, Granular Dynamics, Celestial Mechanics, Chemistry, Condensed Matter Physics, Planetary and Computer Sciences, to name the main ones, in order to understand the data collected and analysed by observational astronomy (visible, thermal, and radio), and different space missions. In this paper, we present a review of the multi-disciplinary research carried out by these different scientific communities in an effort to study SSSBs.