If one adds more particles to a cluster, the energetically optimal structure is neither preserved nor does it change in a continuous fashion. Instead, one finds several cluster size regions where one structural principle dominates almost without exception, and rather narrow boundary regions in-between. The structure of the solid is usually reached only at relatively large sizes, after more than one structural transition. The occurrence of this general phenomenon of size-dependent structural transitions does not seem to depend on the nature of the particles, it is found for atomic, molecular, homogeneous, and heterogeneous clusters alike. Clearly, it is a collective many-body phenomenon which can in principle be calculated but not understood in a fully reductionistic manner. Actual calculations with sufficient accuracy are not feasible today, because of the enormous computational expense, even when unconventional evolutionary algorithms are employed for global geometry optimization. Therefore, simple rules for cluster structures are highly desirable. In fact, we are dealing here not just with the academic quest for linkages between cluster structure and features of the potential energy surface, but structural transitions in clusters are also of immediate relevance for many natural and industrial processes, ranging from crystal growth all the way to nanotechnology. This article provides an exemplary overview of research on this topic, from simple model systems where first qualitative explanations start to be successful, up to more realistic complex systems which are still beyond our understanding.