Supramolecular chemistry has become an interdisciplinary discipline of chemistry, physics, and biology. As a huge subunit of supramolecular compounds, the functional metal-organic supramolecular systems with well-defined cavities which are able to accommodate size-suitable guests via benign host-guest behavior, have been known as "metalorganic molecular containers" (MOMCs) and attracted much attentions for their rich chemical properties and wide potential applications in molecular recognition, catalysis, biomedical and other fields. In particular, the MOMCs with flexible backbones exhibit a unique feature both in the aspect of structural construction and applications, due to the free rotation and self-adaptively of the specific functional groups in the skeletons. In this paper, we review several selected examples of the coordination-driven metal-organic supramolecular systems from the aspects of self-assembly construction to the various applications. The self-assembly strategies, especially the different choice of organic ligands with flexible backbones during the construction, leading to quite diverse configurations compared to the rigid ligands, have been also discussed to show a different perspective of metal-organic system construction.