Carbon allotropes have contributed to all aspects of people's lives throughout human history. As emerging carbon-based low-dimensional materials, graphyne family members (GYF), represented by graphdiyne, have a wide range potential applications due to their superior physical and chemical properties. In particular, graphdiyne (GDY), as the leader of the graphyne family, has been practically applied to various research fields since it was first successfully synthesized. GYF have a large surface area, both sp and sp2 hybridization, and a certain band gap, which was considered to originate from the overlap of carbon 2pz orbitals and the inhomogeneous π-bonds of carbon atoms in different hybridization forms. These properties mean GYF-based materials still have many potential applications to be developed, especially in energy storage and catalytic utilization. Since most of the GYF have yet to be synthesized and applications of successfully synthesized GYF have not been developed for a long time, theoretical results in various application fields should be shared to experimentalists to attract more intentions. In this Review, we summarized and discussed the synthesis, structural properties, and applications of GYF-based materials from the theoretical insights, hoping to provide different viewpoints and comments.