Exploring the structure of low-dimensional materials is a key step towards a complete understanding of condensed matter. In recent years, owing to the fast developing of research tools, novel structures of many elements have been reported, revealing the possibility of new properties. Refining the investigation of one-dimensional atomic chain structures has thus received a great amount of attention in the field of condensed matter physics, materials science and chemistry. In this paper, we review the recent advances in the study of confined structures under nanometer environments. We mainly discuss the most interesting structures revealed and the experimental and theoretical methods adopted in these researches, and we also briefly discuss the properties related to the new structures. We particularly focus on elemental materials, which show the richness of one-dimensional structures in vacuum and in nanoconfinement. By understanding the binding and stability of various structures and their properties, we expect that one-dimensional materials should attract a broad range of interest in new materials discovery and new applications. Moreover, we reveal the challenges in accurate theoretical simulations of one-dimensional materials in nanoconfinement, and we provide an outlook of how to overcome such challenges in the future.