Molecular containers enclose a well defined cavity in which an appropriate guest molecule can be included. The corresponding complexes are generally characterized by high kinetic stability. Thermodynamic stability can be rather low, however, because attractive interactions are largely missing between host and guest causing binding to be mainly due to entropic factors. This situation can be improved by distributing appropriate binding sites across the inner surface of a molecular container to which an included guest can bind. This approach, while being conceptually simple, is not straightforward since the incorporation of converging binding sites into a concave surface is difficult and usually requires receptors architectures that differ from those of conventional covalently assembled molecular containers. Therefore, the term molecular cage rather than molecular container is often more appropriate for such types of receptors. In this overview, a selection of cage-type receptors is presented whose inner cavity is functionalized with groups that can engage in directed interactions with an included guest. These receptors, classified according to the type of interaction responsible for guest binding, were chosen to illustrate effects of the inwardly directed binding sites on receptor affinity, selectivity, or other binding properties.