Many proteins and nucleic acids, as well as their complexes, consist of structural units with a known internal structure. However, relative position of these units within the entity is often a subject of uncertainty. This problem can be effectively addressed with the help of residual dipolar couplings (RDCs) measured by solution-state NMR in weakly oriented samples. Using a rigid-body approach, the relative orientation of the structural units can be adjusted to match the experimental RDC data. This paper explains why the rigid-body approach is well suited for application with the RDC data and discusses the general algorithm suitable for such studies. The examples of RDC-based rigid-body treatment involving protein backbone fragments, RNA helices, multidomain proteins, protein-ligand systems, and protein complexes are described in detail. The discussion includes systems where multiple structures co-exist in a dynamic equilibrium. Various degeneracies associated with the RDC data are considered and the methods that can assist in resolving the ambiguities are described.