The conceptual idea of molecular container compounds and their synthesis has opened an entirely new and very interesting research field: the chemistry of and within molecular container compounds and their complexes. Molecular containers have inner phases just large enough to accommodate a single guest molecule. Beginning with Donald J. Cram's first synthesis of a carcerand, which permanently entrapped a single guest molecule, many other containers such as hemicarcerands, molecular lantern, self-assembled capsules and fullerenes have been synthesized and studied. Not only is the design and development of new container compounds an ongoing challenge for organic chemists, but also the systematic investigation of chemical reactions within their inner phases. The results of a large variety of inner phase reactions spanning acid-base, reduction, oxidation, nucleophilic substitution, addition, thermal, photochemical and pericyclic reactions have provided us with more insight into the relationship between bulk phase and inner phase reactants and the mechanism of the transfer of electrons and photons through the insulating shell of a container molecule. They have also led to very spectacular applications of molecular container compounds such as the stabilization of reactive intermediates by incarceration. These highlights of inner phase chemistry and the current efforts and successes towards using molecular containers as catalytic reaction vessels are presented and discussed.