Small bodies are among the best tracers of our Solar System's history. A large number of space missions to small bodies (past and future) offer a unique opportunity to use these bodies as a natural laboratory to study the different processes, mechanical structures, and responses that drive the origin and evolution of small bodies, which are connected to the origin, evolution, and current architecture of the Solar System. Images of small bodies sent by spacecraft have revealed unexpectedly rich and complex geological worlds. In addition to very diverse compositions, small bodies in the Solar System have highly diverse shapes and structures, which reflect both different evolutionary paths and material properties. Furthermore, each individual body has diverse geological features on its surface, which include craters of various sizes and depths, boulders of different sizes and morphologies, lineaments, fractures, pits, signatures of landslides, terraces, and ridges. Such a geological richness could not be detected via ground-based observations, and we are still at the beginning of understanding their significance on the low-gravity surfaces on which they manifest. The combination of space mission data and numerical modeling allows us to enrich our understanding of the origin, evolution, and physical properties of these fascinating bodies. For instance, starting from the shape models, bulk densities, and spin rates determined from space mission data, we can investigate the formation mechanisms that lead to the observed properties of small bodies. We can also infer the interior and mechanical properties (e.g., friction and cohesion) that allow a small body to be structurally stable, as well as its further potential evolution under processes such as a spin rate increase or an impact. Then, considering the various processes that these bodies experience during their evolution, we can investigate how these processes modify their properties and, in turn, how those properties influence the outcome of these processes. This paper reviews our current knowledge of small-body shapes and structures and discusses the various processes that are responsible for their formation and evolution, which can modify the characteristics of the bodies. We separately consider each population of small bodies, although in some cases, such as active asteroids and comets, the distinction between two populations solely in terms of physical properties is not clear. We then summarize the main findings regarding the physical properties of small bodies that have been the target of rendezvous or sample return missions.